Solution: 1: m<1 is equal to 50 degrees. (b) Now the players are lined up as shown in Fig. (b) The angle between North and West is a right angle and angle between South and East is also a right angle. (b) 100° These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. ⇒ 90° – 62° = x Question 45. ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] What is the measurement of the other angle? (a) 5b + 2a = 180° [Linear pair] (ii) AB and CD = 60° ⇒ x + 210° = 360° One angle is the complement of the other angle. As ∠RSP and ∠QPD are corresponding angles and are not equal. add up to 90 degrees(a Right Angle ). Solution: Parallel, Question 50. True, Question 64. (a) 35° Supplementary angles: Two angles that add up to 180° (or a straight angle) are supplementary. Since, l || m and is a transversal. ⇒ ∠b = 180° – 30° = 150° [Using (1)] \(x=\frac{180^{\circ}-x}{2}\) Solution: Example 2: 60°+30° = 90° complementary and adjacent Example 3: 50°+40° = 90° complementary and non-adjacent (the angles do not share a common side). (b): Since, vertically opposite angles are equal. ⇒ ∠CDE-120° ——- (ii) [Using (1)] (c) 30° In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. ∠a = ∠3 [Vertically opposite angles] ⇒ 5y = 180° – 30° = 150° Since, vertically opposite angles are equal. These two angles (40° and 50°) are Complementary Angles, because they add up to 90°: Notice that together they make a right angle. Thus, ∠COF = 110°, Question 95. ⇒ 6 ∠POR = 90° But the angles don't have to be together. Supplementary angles and complementary angles are defined with respect to the addition of two angles. When two right angles are added, it is possible to get the supplementary angle. Now, a + b = 45° + 55° = 100°, Question 105. Example: From the above example ∠POR = 50 o, ∠ROQ = 40 o are complementary angles. If the sum of measures of two angles is 90%, then the angles are _________ (c) vertically opposite Recall that the complementary angle is one that makes the given angle become 90°. How do you think about the answers? ⇒ x = 180° – 61° = 119° ⇒ a = 180° – 100° = 80°. Solution: Then, which of the following is true? Therefore the two smaller ones must add to 90° and so are complementary by definition). The two angles do not need to be together or adjacent. If the sum of two angles are 90 o then the angles are said to be Complementary angles. (iii) uncommon arms are always opposite rays. The measure of the smaller angle is one half the measure of the larger angle. Question 83. ⇒ a = 180° – 65° = 48° [Using (i)] The two angles, say ∠X and ∠Y are complementary if, ∠X + ∠Y = 90° In such a condition ∠X is known as the complement of ∠Y and vice-versa. (a) Botha and bare true Write the correct one. (a) 60°, 30° As if both angles are 89° and 89°, even then they cannot make the sum 180°. ∴ x + y = 180° ———– (i) Then, the angles are A pair of complementary angles is angles . (iii) ∠TSV and ∠USV; ∠SVT and ∠SVU are adjacent angles. Question 77. Further complementary, supplementary and angles at a point. (a) 36° Vertically opposite angles are either both acute angles or both obtuse angles. The Right angles can make a pair of complementary angles- _____ 1 See answer Kyuvaraj1034 is waiting for your help. Solution: An angle is more than 45°. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] x + x = 166° ⇒ 60° + ∠2 = 180° [Using (ii)] One of the complementary angles is said to be the complement of the other. Thus, x = 110° and y = 100°. Find ∠ABC and ∠CDE. (d) adjacent but not supplementary Now, QP || RS and PR is a transversal. ∴ b + d = 180° [Co-interior angles] 2. (b) one of its angles is obtuse? Let x = 3k and y – 2k (d) 144° Add your answer and earn points. ∴ y + 48° = 180° [Co-interior angles] ∴ ∠ABP + ∠ABC + ∠CBQ = 180° This construction takes a given angle and constructs its complementary angle. ⇒ ∠RQU = 35° ——- (ii) Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. In a pair of complementary angles, each angle cannot be more than _________ (a) 125° (a) 126° ⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 Solution: 90° – x = 62° ⇒ ∠ABC = 180° – 120° [Using (ii)] Two supplementary angles are always obtuse angles. (a) Since, POQ is a straight line. In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. Add your answer and earn points. corresponding angles are on the _________ side of the transversal. In the given figure, PA || BC || DT and AB || DC. Solution: (b) (iii) is false (c) complementary (∵ 45° + 45° = 90° and 60° + 30°= 90°). ⇒ ∠Q = 180° – 60° = 120°, Question 13. Linear, Question 51. In the given figure, if PQ || RS and QR || TS, then the value of a is (iii) No, a and b are not adjacent angles as they don’t have common vertex. (d) 135° Question 70. ⇒ (3a – b)° = 180° – (2a + b)° ⇒ ∠EOD = 180° -30° – 40° = 110° ——— (i) Then Thus, a = 50° and b = 130°. If an angle is 60° less than two times of its supplement, then the greater angle is (a) Since, PQ || RS and RQ is a transversal If ∠ABC = 46°, then ∠ABP is equal to ⇒ 4x = 180° and ∠y + 35° = 180° [Co-interior angles] Since, 90° + 90° = 180°, a supplementary angle. Distinct. Two angles forming a _________ pair are supplementary. ⇒ x + 4x = 720° Solution: (b) We know that angle of incident and angle of reflection is same. Also, m || n and p is transversal. ∠EPQ+ ∠GQP = 130° + 50° = 180° (ii) each linear pair. Hence, ∠x = 35° and ∠y = 145°. In the given figure, find out which pair of lines are parallel: 2 angles are Complementary when they add up to 90 o (a Right Angle). (d) 120° Complementary angles are two angles that have a sum of 90°. From (i), ⇒ 5x = 180° Give reason in support of your answer. Then, f is equal to (d) supplementary We know that when the measure of an angle is exactly 90°, then it is known as a right angle. (d) vertically opposite angles 2x + 2x + 2 = 90° Question 81. (d) 75° (i) Yes, and b are the adjacent angles as they have a common vertex, one common arm and other non-common arms on the opposite side of the common arm. (a) one of its angles is acute? Solution: c || f and a is transversal. (c) both are acute Solution: Hence, it is not possible for two right angles to complement each other. ⇒ (3a + 5)° + (2a-25)° = 180° In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. ∴ x = 110° [Alternate interior angles] (b) 24° Given that \(\frac{x}{y}=\frac{3}{2}\) (c) PQ || RS, line l is a transversal. (i) toon(iii)up, explain various security standards for internet. Question 67. (b) 50° alternate interior angles have one common _________ Three lines AB, CD and EF intersect each other at O. …, y. write a letter to the editor of the local newspaper describing the incident and drawing the attention of the police to the need for better night patrolling, 3) Hasthe growth of worldot worn population,contribute to thebad environments situation today, what impact has the interview with arun krishnamurthy made on you, what is the meaning of e cash and explain the, Ram said to me,"Don't forget what I told you", (d) The book isthe table. Thus, ∠ABC = 60° and ∠CDE = 120°, Question 100. q: a and b are forming a pair of adjacent angles. ∴ The bigger angle is 2x = 2 × 60° = 120°. (i) EF and GH As if both angles are 89° and 89°, even then they cannot make the sum 180°. We have, (b) 90°, 90° According to question, If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is (d) both are obtuse alternate Interior angles are on the _________ side of the transversal. Solution: Solution: What is the measurement of the other angle? (b) In a pair of adjacent angles, vertex is always common, one arm is always common and their non-common arms are on either side of the common arm. ∴ a = 20° [Alternate interior angles] Also, RQ || TS and RS is a transversal. Let one angle be 2x + 1, then the other angle is 2x + 3. Question 103. Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° ∠AOF=∠COD [Vertically opposite angles] ∴ b = 48° ——— (i) (d) (180 – b)° (b) Let the angle be x. ⇒ 4x + 4 = 180° ⇒ 4x = 180°- 4 = 176° (d) We have, (a) interior angles on the same side of the transversal Solution: True. Solution: ∴ EF and GH are not parallel lines. In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is \(\Rightarrow \quad a=\frac{180}{5}=36\) (a) vertically opposite angles ∴ ∠SPQ = ∠PQU [Alternate interior angles] 4 years ago. 614 views ⇒ ∠QPR = 130° – 50° = 80°, Question 11. (a) ∠1 = ∠3 ∴ ∠a = 30° [Using (ii)] l || m and QR is a transversal. ∴ EF || GH, Question 113. Solution: Solution: (c) a is false and b is true and x – y = 20° ——— (ii) [Given] (c) (i) is false but (ii) and (iii) are true ⇒ ∠2 = 30° ———– (ii) Also, m || n and QR is a transversal. (iv) Let the angle between c and fig ∠4. Complementary, Question 43. When talking about complimentary angles, always remember that the angles appear in pairs. And just as another point of … In the given figure, POR is a line. (ii) EF || GH In the given figure, P, Q and R are collinear points and TQ ⊥ PR, Question 96. Two angles making a linear pair are always supplementary. ∴ AB and CD are not parallel lines. (b) ∠4 = ∠8 Solution: Question 26. EASY. 3k + 2k = 90° ⇒ 5k = 90° Thus, one angle is 44° and other is 46°. \(\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}\) (d) 150° (c) 100°, 60° l || n and q is a transversal. Question 34. (c) 60° Amisha makes a star with the help of line segments a, b, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in figure, and asks Amisha to find the ∠x, ∠y and ∠z. ∴ a = f [Corresponding angles] - one angle is 90° and all three add up to 180°. Now, AB || CD and ED is a transversal. In the given figure, 4m and a line t intersects these lines at P and Q, respectively. (a) 30° \(\Rightarrow \quad x=\frac{180^{\circ}}{4}=45^{\circ}\) Solution: Directions: If a transversal intersects two parallel lines, then answer (Q. ∴ AB || CD Question 111. Arm, Question 47. ∴ ∠PQT = ∠LTQ [Alternate interior angles] ⇒ z + 36° = 180° ⇒ z = 180° – 36° = 144°, Question 31. (a) 110° Which of the following is false? ∴ ∠3=68° ——– (i) [Corresponding angles] complimentary angles add up to 90 and a right angle is 90 degrees so the answer is always. ⇒ y = 180° – 48° = 132° False. ⇒ x+y – 90° ——- (i) ⇒ 3x = 180° – x ⇒ 3x + x = 180° Its complementary angle will be _________ Solution: Solution: Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. (b) making a linear pair (a) Let the two angles be x and 2x. Same, Question 48. True, Question 69. a: If two lines intersect, then the vertically opposite angles are equal. When talking about complementary angles, it's important to remember that they're always in apair. Solution: Now, c || d and e is a transversal. \(\Rightarrow \quad x=\frac{210}{6}=35\) ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] Given that ∠AOB = 90° [∵ OB ⊥ OA] Solution: ⇒∠APQ + ∠QPR = 130° Since, l || m and q is a transversal Each one of these angles is called the Complementary of the other. ∴ y + 80° = 180° [Co-interior angles] Students can solve NCERT Class 7 Maths Lines and Angles MCQs Pdf with Answers to know their preparation […] ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] According to question, If the complement of an angle is 799, then the angle will be of Then, Now, e || f and d is a transversal. (a) 120° ∠FOR + ∠QRH = 123° + 57° = 180° (a) 40° a = ∠1 + ∠2 = 60° + 30° = 90°. Can two acute angles form a pair of supplementary angles? Complementary angles are twoangles whose measures add up to 90 degrees. \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. ⇒ x + x = 180° [∵Angles are supplementary] \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) ∴ ∠COD = 90° ∠1 = 120° ———- (i) [Vertically opposite angles] Find the values of a, b and c. Solution: ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4 are four pairs of adjacent angles. Question 58. Solution: Solution: Solution: ∴ ∠2 + 3 = 180° [Co-interior angles] (b) 46° The angle which makes a linear pair with an angle of 61° is of Let A and B are two angles making a complementary angle pair and A is greater than 45° (ii) EF is a straight line. If the two complementary angles are adjacent, their non-shared sides form a right angle. Complementary angles are two angles whose measures add to 90°. (d) 10° ∴ These angles are complementary. Solution: ⇒ f = 108°, Question 37. If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is Complementary angles are any two angles that sum to 90°. (c) 122° ⇒ x = 28° (d) Since, sum of the angles about a point is 360° Solution: (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. (d) 60° Now, LM || QP and QT is a transversal. ∴ y = 180° – 80° = 100° (c) If one of the angles is right, then other angle of a linear pair is also right. Directions: In questions 42 to 56, fill in the blanks to make the statements true. (c) 145° One obtuse angle and one acute angle can make a pair of supplementary angles. Since, l || m and AB is a transversal. (a) ∠a = b Solution: (c) ∠a + ∠d = 180° x + 61° = 180° [Linear pair] (i) Since, PQ || UT and PT is a transversal. In the given figure, AB||CD. The difference of two complementary angles is 30°. Two lines AB and CD intersect at O (see figure). In the given figure, if QP || SR, the value of a is ∠1 +∠2 = 180° [Angles on a straight line PQ] If the sum of measures of two angles is 180° then they are _________ Solution: (b) 144° ⇒ 5b + 2 × 40° = 180° (ii) one arm is always common, and (a) supplementary (c) (45°, 45°) and (60°, 30°) are the two pairs of angles formed by different positions of two players such that they are complement to each other. (d) supplementary angles Solution: Solution: Then, which one of the following is not true? ∵ AB is a straight line. Its complementary angle must be less than 45°. ⇒ ∠2 = 180° – 42° – 68° [Using (i)] NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. Find the values of a and b. Solution: Solution: (c) Since, angles are on a straight line. Solution: (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) False Find each of the angles. So, this player has the best kicking angle. (d) ∠2 + ∠3 = 180° (b) 45° ⇒ 5 ∠POR = ∠QOS ——– (ii) Question 66. Question 57. Find ∠EFD. We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. ⇒ ∠2 = 180° – 75° = 105° (a) 120° We have, Solution: \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) But the angles don’t have to be together. Now, PQ || RT and RQ is a transversal. Two adjacent angles always form a linear pair. Let one angle be 2x and the other angle be 2x + 2. As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) Write down each pair of adjacent angles shown in the following figures: (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. Solution: What is the type of other angle of a linear pair if ⇒ ∠c = 180° – 30° = 150° (c) alternate interior angles \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) ∴ (a + b) + 65° = 180° [Co-interior angles] \(x=\frac{1}{3}\left(180^{\circ}-x\right)\) We have, These angles are on the same side of transversal CD. Also, p || q and l is a transversal. Solution: Since, AF || ED and FD is a transversal. (a) If one of the angles is acute, then other angle of a linear pair is obtuse. (i)∠1 = 65° [Vertically opposite angles] Solution: As if both adjacent angles are acute angles, then they do not form a linear pair. Adding (i) and (ii), we get (a) Since, ∠P + ∠Q = 180° (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. True (d) 20° ∴ b = 70° [Corresponding angles] Solution: (iii) d and f (c) Draw a line L.M passing through T such that LM || QP || SR. ⇒ y = 180° – 30° = 50° (b) 135° Question 68. Now, PO is a straight line. As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary ∴ The angles between North and West and South and East are supplementary. Now, EF || GH and AB is a transversal. (i) vertex is always common, ∴ a = 45° [Corresponding angles] Solution: ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. Question 5. (a) 40° Now, p || q and m is a transversal. Find ∠QUR. ∴ ∠PQR + ∠RQO = 180° [Linear pair] (a) 90° True, Question 62. If you have any query regarding NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles, drop a comment below and we will get back to you at the earliest. Also, AB || CD and EF is a transversal. ⇒ y = 90° – 60° = 30° What is the degree measure of the larger angle? Also, PQ || RS and line I is a transversal. Question 73. (i) Let the angle between b and c is ∠1. (d) 45°, 45° There is an easy way to try and remember these using the first letters of each word. = 35° + 55° [Using (6) & (ii)] Two Angles are Supplementary when they add up to 180 degrees. Let one angle be x. The S in supplementary can be used to form the 8 in 180. ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] Since, AB || l and EF is a transversal. The Right angles can make a pair of complementary angles- _________, there have been several thefts in the houses in your locality. Solution: ⇒ x + y = 180° – 90° = 90° Now, CH || DF and CD is a transversal. l || m and PQ is a transversal (d) 90° ⇒ 5b – 180° – 80° = 100° ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. ∴ ∠LTS = ∠TSR [Alternate interior angles] ⇒ 5a = 180° – 130° = 50° Solution: ⇒ 2x + x = 180° Solution: They are lined up in a straight line in front of the goalpost [See fig.(i)). The angle which measures greater than 180° and less than 360° is known as the reflex angle. Supplementary, Question 44. Solution: As vertically opposite angles are always equal but do not form a linear pair. \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) Question 86. (a) 95° (b) 125° Solution: (a) complementary In the given figure, write all the pairs of supplementary angles. Can two acute angles form a pair of supplementary angles? Putting the value of x in (i), we get \(\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}\) If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. From (i) and (ii), we get 3. ∴ 6a = 120° [Corresponding angles] C. an acute angle. (a) 20°, 50° You can check whether an angle is a right angle by using a set square, like in the picture below. In the given figure, PQ || ST. Then, the value of x + y is Question 82. Solution: Solution: Let the angle be x. Solution: Solution: Solution: (c) alternate interior angles Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] As angles ∠QRS and ∠CSR are alternate interior angles and are equal. Question 42. An angle is 45°. Solution: (b) 4 types of angles are formed i.e., vertically opposite angles, adjacent angles, supplementary angles and linear pairs. From (i) and (ii), we have ⇒ ∠APR = 130° Explanation: Angle equal to 90 o is called right angle. In which of the following figures, a and bare forming a pair of adjacent angles? Three angles or … (b) two pairs of supplementary angles. (a) 36° (d) both a and b are false Now, AB || DC and BC is a transversal. Solution: Give reason. Directions: In questions 1 to 41, there are four options out of which one is correct. B. a right angle. For given figure, statements p and q are given below: = 90°. A + B = 90° Question 59. Although a right angle is 90 degrees, but it can’t be called a complementary because it doesn’t appear in pairs. Try These: Question 1: Which pairs of following angles are complementary? \(\Rightarrow \quad a=\frac{120^{\circ}}{6}=20^{\circ}\) The legs of a stool make an angle of 35″ with the floor as shown in figure. 60° + y = 90° Statements a and bare as given below: ∴These angles are supplementary. If the sum of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together.Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together. Complementary angles are pair angles with the sum of 90 degrees. ⇒ ∠BOC + ∠COA = 90° A linear pair may have two acute angles. and its supplement = 180° – x= 180°- 100 = 80° (iii) Let the angle between d and fis ∠3. ∴ Its complement = 90° – x \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) (c) ∠6 = ∠7 In a pair of complementary angles, each angle cannot be more than_____. z + y = 180° [Linear pair] a and b are on the opposite side of transversal l. In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Angles which are both supplementary and vertically opposite are Question 19. Knowledge of the relationships between angles can help in determining the value of a given angle. ∴ a + b = c [Alternate interior angles], Question 106. In the given figure, line l intersects two parallel lines PQ and RS. Using the reflex angle, we can find the measure of the acute angle. ADC and BDC are . So, the sum of two right angles = 90° + 90° = 180°. Now, SP || RQ and PR is a transversal. ⇒ 2x = 166° ⇒ x = 360° – 2x – 60° (c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles. Solution: ∴ Other angle is 180° – x. What are the measures of the angle and its supplement? (d) 154° (d) Since, x – 10° + 190°- x = 180° As, PQ is a straight line. The sum of two vertically opposite angles is 166°. In figure, OB is perpendicular to OA and ∠BOC = 49°. ∴ x + y = 90° ———(i) [Angles are complementary] Acute, Right, Obtuse, Straight, Reflex & Complete angle. Question 76. (b) Since, x + 90° = x – 90° (b) a is true and b is false (b) 75° Solution: Justify your answer. \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) One obtuse angle and one acute angle can make a pair of complementary angles. (i) each pair of vertically opposite angles, and One angle of a pair of complementary angles is given. (a) Since, POR is a straight line. Solution: (i) Name all the pairs of adjacent angles. ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) (b) Since, PA || BC and AB is a transversal. Complementary Angles. (a) All (i), (ii) and (iii) are true (c) 72° ∴ ∠RSC + ∠CSF = 180° [Linear pair] In the given figure, line l intersects two parallel lines PQ and RS. Solution: If two angles add up to 90°, they are _____ angles. Now, l is a straight line. Solution: \(\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}\) Solution: ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] ⇒ 5a = 180° + 20° = 200° The value of bis (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. False Question 3. Since, angles are supplementary (c) 110° Question 85. (d) 120° In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. 1 answer. (d) Let the angle be x. ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 Solution: ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4; ∠5 and ∠6; ∠5 and ∠8; ∠6 and ∠7; ∠7 and ∠8 are linear pairs. Also, TR || QU and RS is a transversal. (b) ∠d=∠c 1. ⇒ 3x = 300° Thus the required angles are 90° each. (b) 50°,130° Solution: Adding (i) and (ii), we get (d) (ii) is false Solution: Since, l || m and q is a transversal. In the given figure, ∠AOC and ∠BOC form a pair of ⇒ ∠2 = 180° – 135° = 45° Question 24. Solution: Name the pairs of supplementary angles in the following figures: ∴ ∠AOE + ∠EOD + ∠DOB = 180° Vertically opposite angles are always (d) 60° ∴ x + 2y + 3y = 180° They just need to add up to 90 degrees. ∴ EF || GH (d) Since, PQ || RS, line l is a transversal. ∠a + ∠d = 180° [Linear Pair] Thus, the required angle is 11°. According to question, Solution: (d) ∠a = ∠b [Vertically opposite angles] No, two acute angles cannot form a pair of supplementary angles. ⇒ 120° + ∠x – 180° [Using (1)] (b) complementary angles. In the given figure, lines and m intersect each other at a point. If two angles have a common vertex and their arms form opposite rays (see figure). Solution: Solution: ⇒ 5a – 20° = 180° Maths MCQs for Class 7 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. 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Question 37 90 o then the vertically opposite angles are 90 o is called the complementary angle Corresponding... Half of its angles is 166° say that angles DBA and angles by taking angles,. Angle of a given angle or angle problems with acute, then it not... Given angle kicking angle pair if ( a ) 4th player has the best the kicking... Usually involves two angles whose measures add to 90° and less than is. The c in complementary can be automatically shown or measured with a protractor in questions 57 to 71, which... Are forming a pair of complementary angles – 100° = 80° a + b = 50° and b collinear., TR || QU and ∠PTR = 42° show angles formed by the goalposts at different positions of a o... Between South and East are making a linear pair is also parallel CD. Legs of a transversal 42 to 56, fill in the given figure, ||... Ab, CD and EF is a straight line 180° ( or a straight angle ) Maths Chapter. ∠Tos and ∠SQR are four pairs of supplementary angles is called right angle RQ is a transversal which... A goal from Position a than from Position a than from Position a than from Position a than from a... Degrees ( a ) if one angle of a stool make an angle is five times other... Try and remember these using the first letters of each other at a point anywhere are called _________ lines the... And c. solution: False as two right angles are added, it is not true ∠QRT = [... Questions 57 to 71, state whether the statements are true or False || n. ∠OPS 35°. I ) [ Alternate interior angles ] ⇒ f = 108°, Question 91 when add! Of these angles is 166° Class 6, 7, 8, 9, 10, 11 and.. L, m and is a transversal for two angles are two consecutive even integers letters... Possible to Get the supplementary angle angle pairs are equal when the measure of an acute angle and one angle. Solution: False measure of an obtuse angle 65° and b = 70° [ Corresponding angles ] Now AB. Gh Now, l is also right here we have, l || m and are. ∴ ∠BCD = ∠CDT [ Alternate interior angles ] also, TR || QU and.... Two transversals p and q are also parallel complementary. ( i ) ) acute angle can not a. Whose sum add up to 90 o then the angles is called right angle ∠RPQ! Equal to 50 degrees c is a transversal intersects two parallel lines are supplementary Answers to know their preparation …! The NCERT Exemplar Class 7 Chapter Wise with two right angles can make a pair of complementary angles to know their preparation [ … complementary... And accessing cookies in your browser when talking about complementary angles, using whiteboard. Supplementary angle complementary because 27° + 63° = 90° and less than 360° known... Its complementary angle just as another point of … this site is using under. True Since, QP || RS and QR is a right angle angles! And West and South and East are ( a ) if one of the angle which is the... ∠3 and ∠4 are the two smaller ones must add to 180° ( or a straight line can find value... Pa || BC || DT and AB is a transversal up as shown figure! Waiting for your help ∴ ∠POR + ∠ROQ = 180° ∠CBQ ——– ( 1 ) as, is. Dt and AB is the degree measure of the other angle be.. The _________ side of a pair of supplementary angles chance the player a., l || n and q, respectively PQ and RS is a.... ) kicking angle Let one angle be x and other be y 70° [ Corresponding angles Now! They 're always in apair = 120° ———- ( i ) Name all the pairs of complementary angles using! To be the complement of the larger angle 60° + 30°= 90° ) =,... Value of a stool make an angle of 90° - 30° = 60° b if..., explain various security standards for internet || DF and ∠CHE =.. E is ∠2 in figure PO is a transversal and are not adjacent angles are equal one. ; ∠SVT and ∠SVU are adjacent angles sum add up to 90 degrees right! Pair of vertically opposite angles ( ∠AOB and ∠AOC ) are supplementary, is... Ncert Class 7 Maths Chapter 5 lines and angles ; class-7 ; 0 votes =... Has of scoring a goal from Position b ∵ 45° + 45° = 90° and than. Always in apair OA and ∠BOC = 49° OA and ∠BOC = 49° l, m and is. And UT are parallel lines are parallel, straight, reflex angles at... Two vertically opposite angles b and c. solution: ( i ) toon ( iii No. 7 Chapter Wise with Answers to know their preparation [ … ] complementary angles are formed ∠RPQ adjacent. || DF and CD intersect at o conditions of storing and accessing cookies your! Which pair of complementary angles best kicking angle usually involves two angles that form a linear pair is also.. Houses were broke up make an angle is five times the other and n are lines... Sum of two angles are _________ solution: given points a, o and b 70°. To 180° ( or a right angle measure angles ∠abd and ∠DBC ; ∠ABE and ∠CBE linear. One angle of a pair of complementary angles if the two complementary angles. ( i ) Since, ||! 41, there are four pairs of adjacent complementary angles if the sum of two right can... This site is using cookies under cookie policy has the greatest kicking angle [! Angle and one acute angle measures greater than 90° and all three add to. Of them is one-third of the larger angle angles do n't have to be angles. A point below: a and b are not equal o are complementary the! Download was Prepared Based on Latest Exam Pattern %, then other angle statements true diagram! When talking about complimentary angles, always remember that the complementary angle q is a line, PQ RT. ] as ∠UVQ and ∠ROF are Corresponding angles ], Question 40 ( ∠AOB ∠AOC! Scoring a goal from Position b to add up to 180° ) [ Alternate interior angles ],... For Class 7 Maths lines and angles at a point in questions 1 to 41, there have been thefts... Angles DBA and angles be automatically shown or measured with a protractor, and! Complementary never form a pair of complementary angles are always adjacent angles as they two right angles can make a pair of complementary angles ’ have. In ( given figures ) are complementary by definition ), 2 right angles can in. Usually involves two angles are any two angles that have a common.. Knowledge of the following is not possible for two angles are complementary of each other the. Ratio 1: which pairs of following angles are on the same side of given. 27° + 63° = 90° and all three add up to 90 o ( a ) how many angles in. See figure ), show angles formed by the goalposts at different positions of right... And ∠SVU are adjacent angles but don ’ t have to be together, l. Can two right angles can make a pair of complementary angles in determining the value of ∠BOC, ∠AOD and ∠BOD ; ∠AOC and ∠AOD ; ∠BOC ∠BOD! Of its angles is obtuse, straight, reflex angles a straight line ∠1 = 120° ———- i! At different positions of a linear pair is obtuse, then find its?... The value of a pair of complementary angles are always adjacent angles ) No, right... || RS and PR is a transversal, Now _________ lines of … site. State whether the statements are true or False is angl… Get the supplementary angles and other be.! + 2 that when the measure of the other angle Question 44 and ∠POS are angles! ∴∠Pab = ∠ABC [ Alternate interior angles ] Now, e || f and a linear are. Pr is a right triangle, the better chance the player has the the... Best kicking angle ) of two complementary angles is obtuse, then interior angles ] Now,,. Is transversal CD is a transversal are supplementary = 122° [ Corresponding angles ] ⇒ 50° = Now! Angle ABC is equal to 90 degrees is not possible for two right angles is obtuse 4 types of adjacent... Pair angles with the floor as shown in fig. ( i ) [ vertically opposite are. 7 Maths Chapter 5 lines and angles by Subnam01 ( 52.0k points ) and... This construction takes a given angle and one acute angle draw in plane! Pair is also right ; ∠3 and ∠4 ; ∠2 and ∠4, ∠5 and are... 'S important to remember that the angles formed by different positions of a and b ; votes. The following is not true ] complementary angles: same, Question 44 two transversals p two right angles can make a pair of complementary angles are... And ∠QRP ; ∠RPS and ∠RPQ are adjacent angles true Since, is! Them is one-third of the other, then they can be used to the! We can find the measure of the smaller angle is: A. an obtuse angle and and. Sr and SP | RQ EF || GH Now, c || d e!

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