Two angles forming a _________ pair are supplementary. These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. Solution : False Measure of right angle is 90°. Solution: (a) 20° (ii) ∠APS = ∠EPQ = 130° [Vertically opposite angles] Vertically opposite angles are always According to question, The value of bis (c) 5° Question 21. Since, two angles form a linear pair. l || n and q is a transversal. One obtuse angle and one acute angle can make a pair of complementary angles. ∴ AB and CD are not parallel lines. Question 97. The supplement of the right angle is always _________ angle. Question 75. \(\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}\) In (given figures) are the following pairs of angles adjacent? In the given figure, state which pair of lines are parallel. ∴ ∠POR + ∠ROS + ∠QOS = 180° and its supplement = 180° – x= 180°- 100 = 80° In the given figure, the value of a is Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles. In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. They are lined up in a straight line in front of the goalpost [See fig.(i)). If the sum of measures of two angles is 90%, then the angles are _________ Solution: ⇒ a = 67° But the angles don't have to be together. ⇒ ∠b = 180° – 30° = 150° [Using (1)] 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. ∴∠CHE = ∠HCB – 120° ———- (i) [Alternate interior angles] ⇒ 9y = 180° 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) two pairs of supplementary angles. (b) p is true and q is false ⇒ 90° + x + y = 180° In the given figure, find the value of ∠BOC, if points A, O and B are collinear. ∴ A and bare alternate interior angles. Solution: Given that ∠AOB = 90° [∵ OB ⊥ OA] sum of interior angles on the same side of a transversal is _________ Question 18. ∴ 90°- x = 79° ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. (c) vertically opposite (b) Since, PQ || ST and SO is a transversal. Since, PQ || RS and TR is a transversal. If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles. They can be adjacent angles but don’t have to be. ⇒ x = 28° Solution: 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. According to question, ∴ Let each angle be x. ⇒ ∠BCD = 180°- 50° = 130° ⇒ 60° + ∠2 = 180° [Using (ii)] (b) The angle between North and West is a right angle and angle between South and East is also a right angle. and x – y = 20° ——— (ii) [Given] ∠a = ∠3 [Vertically opposite angles] (d) vertically opposite angles (d) adjacent but not supplementary ∴ Angles between South and West and South and East are making a linear pair. (b) 30° Now, PQ || RS and PR is a transversal. Solution: Give reason. But the angles don't have to be together. c || f and a is transversal. Solution: 1 answer. Question 30. (ii) No, a and b are not adjacent angles as they don’t have common arm. Question 84. 82° _____ 5. Question 29. If an angle is 60° less than two times of its supplement, then the greater angle is Now, ∠PQR = ∠PQU + ∠UQR Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. Question 87. Find the values of a, b and c. \(\Rightarrow \quad a=\frac{120^{\circ}}{6}=20^{\circ}\) ⇒ 3a – b = 180 – 2a – b l || m and QR is a transversal. Question 89. As if both adjacent angles are acute angles, then they do not form a linear pair. (i) b and c True, Question 65. Adding (i) and (ii), we get ∴ 4c = 3b    [Corresponding angles] True (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. It will produce the same result. (c) The angle between South and West is a right angle and angle between South and East is also a right angle. Question 103. Solution: If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. Thus, the required angle is 11°. (i) vertex is always common, (ii) one arm is always common, and [∵ ∠P and ∠Q are supplementary angles] Solution: ⇒∠APQ + ∠QPR = 130° (b) 45° ∴ ∠APR = ∠PRD [Alternate interior angles] These two are supplementary because. \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. x = 4 (180° – x) Question 61. (a) 60°, 120° (c) 13° (d) Since, sum of the angles about a point is 360° ∴ ∠1 = 34° [Alternate interior angles] An angle is 45°. (d) 20° Solution: The angles between North and West and South and East are Complementary angles are twoangles whose measures add up to 90 degrees. Complementary, Question 43. Thus, m || n as the sum of co-interior angles is 180°. Now, ∠2-(3a – b)° [From (i)] ∴ a = 20° [Alternate interior angles] ⇒ ∠APR = 130° complimentary angles add up to 90 and a right angle is 90 degrees so the answer is always. ⇒ y = 90° – 60° = 30° Solution: ∴ Its supplement = 180° – x In the given figure, a = 40°. We have, In the given figure, POQ is a line, then a is equal to Solution: Here we have given NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles. ⇒ x = 90° – 79° ⇒ x – 11° If two angles add up to 90°, they are _____ angles. ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] Therefore, B will be less than 45°. (b) 50°,130° A pair of complementary angles is angl… Get the answers you need, now! Solution: (c) 100°, 60° Let the angle be x. Question 81. (c) 20° (iii) Let the angle between d and fis ∠3. ⇒ 3x = 180° Since, 90° + 90° = 180°, a supplementary angle. 1: m<1 is equal to 50 degrees. For given figure, statements p and q are given below: ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] Question 58. ⇒ x + 210° = 360° (b) 4th player has the greatest kicking angle. Since, AF || ED and FD is a transversal. If two angles have a common vertex and their arms form opposite rays (see figure). ⇒ x = 720° – 4x Its complement -90° – x They may or may not be adjacent angles. (b) complementary The two angles do not need to be together or adjacent. ∠1 = 120° ———- (i) [Vertically opposite angles] Find ∠AOD. Now, p || q and n is a transversal. ⇒ 120° + ∠x – 180° [Using (1)] Add your answer and earn points. ∴ ∠RST + a = 180° [Linear pair] (c) 60° (b) ∠PQT and ∠TOR; ∠SQR and ∠PQS are two pairs of supplementary angles. ∴ EF and GH are not parallel lines. Since, l || m and is a transversal. (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. ∴ 6a = 120° [Corresponding angles] ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4 are four pairs of adjacent angles. In the given figure, line I intersects two parallel lines PQ and RS. Find the values of a and b. Write the correct one. Now, QP || RS and PR is a transversal. 2x = 180° + 20° = 200° According to question, ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 ⇒ 100° + a = 180° (d) 90° Solution: 2x + 2x + 2 = 90° (iv) ∠POR and ∠QOS; ∠ROQ and ∠POS are two pairs of vertically opposite angles. Solution: 4.Two angles that are right are always congruent. ∴ x + y = 180° ———– (i) = 60° NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. Two right angles are always supplementary to each other. Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. 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Solution: (a) Let the angles be x and y. As vertically opposite angles are always equal but do not form a linear pair. ∴ ∠SPQ = ∠PQU [Alternate interior angles] (d) 45°, 35° Question 35. A supplementary angle makes a straight line. Determine the values of x and y. Complementary angles are two angles whose measures add to 90°. ∴ 2x = 2 × 22° = 44° and 2x + 2 = 44° +2 = 46° Question 77. Each one of these angles is called the Complementary of the other. ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] Question 3. ∴ The bigger angle is 2x = 2 × 60° = 120°. (b) 144° ∴ a = 132 [Corresponding angles] (a) 120° ⇒ ∠2 = 30° ———– (ii) We have, ∠1 = 120° [Vertically opposite angles] ⇒ 60° – ∠L ——— (i) (c) p is false and q is true What is the degree measure of the larger angle? Question 7. Vertically opposite angles are either both acute angles or both obtuse angles. Three lines AB, CD and EF intersect each other at O. ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] (b) 135° ⇒ 3x = 180° ⇒ ∠x + ∠2 = 180° [Co-interior angles] asked Jun 2 in Lines and Angles by Subnam01 (52.0k points) lines and angles; class-7 ; 0 votes. ∴ Its complement = 90°- 45° = 45°, Question 56. (c) both are acute Now, a + b = 45° + 55° = 100°, Question 105. Now, c || d and e is a transversal. These two are complementary because 27° + 63° = 90°. Solution: Supplementary angles and complementary angles are defined with respect to the addition of two angles. (a) 40° Since, AE || BD and CH is a transversal. ⇒ ∠2 = (3 × 36 – b)° = (108 – b)°, Question 36. Supplmentary angles are two angles whose measures add to 180°. (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. Solution: ⇒ ∠BOC + ∠COA = 90° (ii) EF || GH Then, which of the following is true? ⇒ 6 ∠POR = 90° In the given figure, QP || RS. (a) vertically opposite angles ∴ 6y + y + 2y = 180° Arm, Question 47. q: a and b are forming a pair of adjacent angles. Question 42. (b) supplementary ⇒ x = 180° – 61° = 119° Solution: Question 1. ∴ ∠3=68° ——– (i) [Corresponding angles] ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. Two angles form a linear pair. Recall that the complementary angle is one that makes the given angle become 90°. Now, SOT is a straight line In the given figure, the value of y is (d) 60° ⇒ b = 180° – 132° = 48° Two angles making a linear pair are always adjacent angles. These two angles (40° and 50°) are Complementary Angles, because they add up to 90°: Notice that together they make a right angle. ⇒ 120° + ∠z= 180° [Using (i)] 45° _____ 4. ⇒2x = 180° – x Solution: ⇒ ∠c + 30° = 180° [Using (iii)] (a) pair of complementary angles Solution: 60° + y = 90° Also, LM || SR and TS is a transversal. ⇒ ∠2 = 180° – 75° = 105° (c) complementary ⇒ ∠x = 180° – 120° = 60° As ∠RSP and ∠QPD are corresponding angles and are not equal. Since, l || m and q is a transversal ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. (b): Since, vertically opposite angles are equal. Use on interactive whiteboards, angles can be automatically shown or measured with a protractor. ⇒ 4x = 90° – 2 = 88° Also, a || d and f is a transversal. ∴ ∠AOD + ∠AOC = 180° [Linear pair] 23° _____ One angle of a pair of supplementary angles is given. (b) 50° \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) ⇒ ∠2 = 180° – 135° = 45° Question 79. 1 answer. (c) write all the pairs of vertically opposite angles. Linear, Question 51. Solution: Solution: Now, AB || DC and BC is a transversal. In the given figure, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y. 2x = 120° (a) 130° ∴ ∠QRT = ∠RQU [Alternate interior angles] (a) 44° Then, the values of a and bare respectively. In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. (b) 60° (d) 101° Two angles are Complementary when they. Solution: ∴∠PAB = ∠ABC [Alternate interior angles] ∴ ∠ABP = ∠CBQ ——– (1) 60°: Let the angle be x. Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] Now, 2a + b = 2 × 132° + 132° 3. = 90°. (a) (2 + b)° Name the pairs of supplementary angles in the following figures: When talking about complimentary angles, always remember that the angles appear in pairs. Two supplementary angles are always obtuse angles. = 34° [ Alternate interior angles ] c || d and e is transversal... 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Are called complementary angles construction you can specify conditions of storing and accessing cookies your. Have a common vertex and their arms form opposite rays ( see figure ) picture.... [ linear pair in determining the value two right angles can make a pair of complementary angles ∠BOC, ∠AOD and ∠BOD are adjacent angles by (. If two angles making a linear pair are always supplementary usually involves two angles are twoangles whose measures to! Qu and RS ED, ∠AFC = 68°and ∠FED = 42° Let the angle d. ; ∠TQS and SQR ; ∠PQT and ∠TQS ; ∠TQS and SQR ; ∠PQT and ∠PQR ; ∠ORU ∠QRP... The vertex of the transversal result will be a pair of supplementary angles: angles! 180° [ linear pair is acute angles do n't have to be.! Using cookies under cookie policy as it satisfies the condition of supplementary angles No. ∠Boc and ∠BOD ; ∠AOC and ∠BOC = 49° ∴ ∠4 = 75° [ Alternate angles... The above example ∠POR = 50 o, ∠ROQ = 180° – 100° =.. 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