In figure, OB is perpendicular to OA and ∠BOC = 49°. ∴ Let each angle be x. Now, QP || RS and PR is a transversal. Two angles making a linear pair are always supplementary. Also, BC || DT and DC is a transversal. 27. Also, m || n and QR is a transversal. True, Question 64. true or false: through any two points, there exists only 1 line. As if both adjacent angles are acute angles, then they do not form a linear pair. Then, which of the following is true? Thus, when two lines intersect, two pair of vertically opposite angles are formed i.e. According to vertical angle theorem, in a pair of intersecting lines, the vertically opposite angles are equal. An angle whose measure is equal to 90° is called a right angle. In the diagram below the two angles α (alpha), and β (beta) are vertical angles and α = β Solution: Question 76. ∴ ∠3=68° ——– (i) [Corresponding angles] Question 32. Comment document.getElementById("comment").setAttribute( "id", "a45dd83c58a54e8143debfefdf41bd5a" );document.getElementById("da6c1f75c6").setAttribute( "id", "comment" ); © MathsTips.com 2013 - 2021. The two vertically opposite angles are always equal. Thus, x = 114° and y = 132°, Question 108. ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] Solution: (a) supplementary (b) equal (c) unequal (d) none of these. Since, vertically opposite angles are equal. Find ∠ABC and ∠CDE. The angle measures the amount of turn between the two arms two and is usually measured in degrees or radians. In each of the following figures, write, if any, An angle that is less than 90 degrees is called an acute angle. (b) a is true and b is false Its complementary angle must be less than 45°. (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. (d) adjacent but not supplementary ⇒ x = 180° – 61° = 119° ∴ a = 20° [Alternate interior angles] Now, c || d and e is a transversal. Now, CD and EF intersect each other at O. the supplement of an obtuse angle is acute. ∴ y = 180° – 80° = 100° The sum of the linear pair of angles is always equal to 180 degrees. Also, AB || DF and BD is a transversal. Solution: In the given figure, POQ is a line. ⇒ 3x = 300° A protractor is an instrument to measure angle. Since, PQ || RT and PR is a transversal. In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. Solution: In the given figure, two parallel lines l and m are cut by two transversals p and 4. A transversal intersects two or more parallel lines. False Correct: The sum is 360°. Solution: 3. 2x + 1 + 2x + 3 = 180° One complete rotation of minute hand in one hour makes angle of ……. ⇒ ∠2 = 180° – 42° – 68° [Using (i)] $$\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}$$ 90° – x = 62° Statements a and bare as given below: (d) 45°, 45° ∴ ∠POR + ∠ROQ = 180° [Linear pair] (d) 105°, 75° ∴ ∠b + ∠1 = 180° [Linear pair] Hence, ∠x = 35° and ∠y = 145°. (b) 135° Two angles making a linear pair are always adjacent angles. (ii) No, a and b are not adjacent angles as they don’t have common arm. Question 3: Look at the figure below. 6. False ⇒ x + y = 180° – 90° = 90° (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. Vertically opposite angles are equal to each other. Solution: Solution: ⇒ x + 210° = 360° Q. (b) 90° Two lines AB and CD intersect at O (see figure). In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. ∴ Its complement = 90° – x We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. (a) Seven football players are practicing their kicks. Question 81. $$\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}$$, Question 17. ⇒ ∠2 = 180° – 75° = 105° Solution: Solution: ⇒ B = 90° – A (d) Let the angle be x. Solution: Answer: True. Question 90. Answer. but ∠4 ≠ ∠8, Question 38. Solution: (a) 20°, 50° ⇒ a = 180° – 65° = 48° [Using (i)] ∴ a = f [Corresponding angles] ⇒ 5b – 180° – 80° = 100° Since, l || m and q is a transversal In the figure below, ABC is a geometrical shape called Triangle (we will know more about triangle in other article). sum of interior angles on the same side of a transversal is _________ (b) PQ is a straight line. Solution: 4. ∴ ∠AOE + ∠EOD + ∠DOB = 180° It is also called semi-circular protractor. ⇒ a = 180° – 85° = 95°. Since, l || m and is a transversal. Question 30. (b) 144° (False) (vi) 30° is one-half of its complement. Now the minute-hand starts moving and an angle is formed between the two hands. Definition and properties of vertical (or opposite) angles. True. As two right angles are supplementary to each other. (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. Question 6. Given that $$\frac{x}{y}=\frac{3}{2}$$ x = 4 (180° – x) (b) complementary angles. $$\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}$$ (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. p: a and bare forming a linear pair. These angles are also known as vertical angles or opposite angles. Solution: ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 (vi) Each interior angle of a n-sided regular polygon is $$\frac{(2 n-4) \times 90^{\circ}}{n}$$. Now, LM || QP and QT is a transversal. Solution: (c) 55° Question 60. In the given figure, lines PQ and ST intersect at O. x + x = 166° (a) supplementary Answer. Question 42. The diagonals of a quadrilateral_____bisect each other. (ii) Let the angle between d and e is ∠2. Question 87. $$\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}$$ ———– (i) ∴ y = 2 × 18° = 36° 45 to 48). ∴ ∠ABP = ∠CBQ ——– (1) Help Amisha in finding the angles. In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. Solution: (b) ∠2 + ∠5 =180° = 264° + 132° = 396°. Now, SOT is a straight line (i) b and c b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. (b) 70°, 40° ∠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. In the given figure, show that Angles may be classified based on their angle magnitude. ∴ Angles between South and West and South and East are making a linear pair. ⇒ x + 4x = 720° (b) ∠2 = ∠4 ∴ ∠c + ∠2 = 180° [Linear pair] ∴ a = 3x = 3 × 36° = 108° Given points A, O and B are collinear. $$\Rightarrow \angle A B P=\frac{134^{\circ}}{2}=67^{\circ}$$. ∴ ∠POQ + ∠QOR = 180° [Linear pair] ⇒ b = 180° – 132° = 48° The angle formed at the vertex B by the two rays AB and BC is called ∠ABC. ∴ b = 55° [Alternate interior angles] 4. 2x + 2x + 2 = 90° False ∴ x + y = 85° + 50° = 135°, Question 41. (i) ∠PSC = ∠RSF = 50° [Vertically opposite angles] ∠1 = 120° [Vertically opposite angles] Question 57. Vertically opposite angles are always For given figure, statements p and q are given below: (c) 79° (ii) EF || GH ⇒ ∠Q = 180° – 60° = 120°, Question 13. If a quadrilateral has three angles of equal measure, then the fourth angle must be a right angle. ⇒ 2∠ABP = 180° – 46° = 134 Question 86. Thus, both the angles are of 83°. ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is (b) 61° Question 1. (b) 30° Question 73. Thus the required angles are 90° each. (c) 110° $$\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}$$ Solution: (c) ∠5 = ∠8 (b) (3 – 6)° 2x = 120° (a) Since, PQ || SR and RP is a transversal (a) (2 + b)° ⇒ x+y – 90° ——- (i) false. ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] ∴ ∠ABC + ∠CDE = 180° [Co-interior angles] degree. (ii) Name all the pairs of complementary angles. (c) making a linear pair (b) 50°, 20° Question 3. (d) Since, PQ || RS, line l is a transversal. Your email address will not be published. Arm, Question 47. In the given figure, PQ, RS and UT are parallel lines. An angle that is greater than 180 degrees is called a reflex angle. In the given figure, if QP || SR, the value of a is In the given figure, PO || SR and SP | RQ. According to question, 1. in a plane, the relation "is perpendicular to" is transitive. Let x = 3k and y – 2k (b) When a transversal cuts two parallel lines, each pair of alternate interior angles are equal. (c) complementary This is the measurement of ∠ABC. ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) Thus, ∠BOC = 40°, Question 101. This is enshrined in mathematics in the Vertical Angles Theorem. $$\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}$$ ∴ ∠RSC + ∠CSF = 180° [Linear pair] 5.if a transversal intersects two lines and the corresponding angles are equal,then the two lines are parallel. Thus, the required angle is 11°. Solution: 2. Solution: Let one angle be x and other be y. ∴ ∠APR = ∠PRD [Alternate interior angles] They have a common vertex. The angles x – 10° and 190° – x are True or False. The Exterior Angle is the angle between a side of a shape AC, and the extended line CD. Question 25. $$\Rightarrow b=\frac{100^{\circ}}{5}=20^{\circ}$$. (i) Name all the pairs of adjacent angles. Write down each pair of adjacent angles shown in the following figures: ⇒ (3a + 5)° + (2a-25)° = 180° ∴ 6a = 120° [Corresponding angles] (d) 30° ∴ EF and GH are not parallel lines. Thus, one angle is 100° and other is 80°. Are Vertical Angles Adjacent? ∴ ∠1 + ∠5 = 180° [By(i)and(iii)] As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary Given that ∠AOB = 90° [∵ OB ⊥ OA] ∴ ∠a = 30° [Using (ii)] Vertical angles are also called opposite angles. If ∠α =30°, find value of ∠β. If they were supplementary, they would not be vertical angles. (a) Since, PQ || RS and RQ is a transversal Then Understanding Trigonometric Ratios With Application to Triangles – Maths Tips. ∴ x + 2x = 180° ⇒ 2x = 166° 2. Now, PQ || RT and RQ is a transversal. Then, which one of the following is not true? Vertical Angles: Theorem and Proof. (a) alternate exterior angles Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. Sources. Find the measure of the segment. Then Two angles whose sum is  90 degrees are called Complementary Angles, Two angles whose sum is  180 degrees are called Supplementary Angles. a and b are on the opposite side of transversal l. Required fields are marked *. Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. 7. Angle e is vertically opposite angle b . Solution: Name the pairs of supplementary angles in the following figures: ∴ x + 64° + 46° +100° – 360° Acute, Question 54. ⇒ 60° + 20 = 180° Solution: Then, angles a and bare respectively ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] ⇒ x = 90° – 79° ⇒ x – 11° As a linear pair has one acute angle and one obtuse angle. Question 112. TRUE or FALSE: The sides of one of two vertical angles are opposite rays to the sides of the other ... About this tutor › true because opposite rays lie on the same line and intersect in only one point. Question 24. (c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles. (b) 46° ⇒ 3x = 180° (b) The angle between North and West is a right angle and angle between South and East is also a right angle. Solution: f = c false . True ⇒2x = 180° – x In the given figure, the value of a is 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. Two angles that share the same vertex and one side are called adjacent angle. The two vertically opposite angles are equal. False True: Then, f is equal to What is the type of other angle of a linear pair if Lines and Angles Class 7 MCQs Questions with Answers. Answer. ⇒ 5y = 180° – 30° = 150° Vertical angles are formed by two intersecting lines. If two supplementary angles are in the ratio 1 : 2, then the bigger angle is Since, AF || ED and FD is a transversal. (iv) c and f Then, Instead, they create CONGRUENT veritcal angles. True False: Q 2: Any two right angles are supplementary. l || m and PQ is a transversal ⇒ x = 150°, Question 10. ... Property: If two lines intersect each other, then the vertically opposite angles are equal. ⇒ 130° = b Now, p || q and n is a transversal. Hence ∠ACD = 60°. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] ⇒ 5a – 20° = 180° and ∠y + 35° = 180° [Co-interior angles] ∴ b + d = 180° [Co-interior angles] (d) 60° Thus, d = 142° (d) 64° We have, Maths Help, Free Tutorials And Useful Mathematics Resources. (a) 95° Solution: ⇒ z + 36° = 180° ⇒ z = 180° – 36° = 144°, Question 31. sometimes. ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. No, two acute angles cannot form a pair of supplementary angles. Question 103. 2x = 180° + 20° = 200° (a) 120° Two right angles are always supplementary to each other. Question 1. Solution: x = 2(180° – x) – 60° ∴ ∠1 = 30° ——– (i) [Corresponding angles] Thus, a = 50° and b = 130°. ∴ Its supplement = 180° – x Solution: (iv) ∠POR and ∠QOS; ∠ROQ and ∠POS are two pairs of vertically opposite angles. True, as all the angles are right angles and the diagonals are congruent to each other. Consecutive interior angles. In the given figure, the value of x is ∠APS + ∠PSC = 130° + 50° = 180° STUDY. ∴ The bigger angle is 2x = 2 × 60° = 120°. Give reason. Solution: Measures (in degrees) of two supplementary angles are consecutive odd integers. Thus, one angle is 89° and other is 91°, Question 99. We have, ⇒ 4x = 90° – 2 = 88° Solution: ∠2 = ∠4 [Corresponding angles] Now, e || f and d is a transversal. False True: Q 4: Any two supplementary angles are adjacent. These angles are always equal to each other. ∴ ∠AOD + ∠AOC = 180° [Linear pair] (Vertical angles such as ... Then one of the alternate angles is an exterior angle equal to the other angle which is an opposite interior angle in the triangle. f = c false ⇒ ∠CDE-120° ——- (ii) [Using (1)] The sum of the Interior Angle and the Exterior Angle are 180°. Question 2. Question 6: Can two obtuse angles form a … If the sum of measures of two angles is 90%, then the angles are _________ C. This statement is true because a triangle cannot have two or more angles that are greater than 60°. Two angles forming a _________ pair are supplementary. Now, AB || CD and ED is a transversal. ∴ Supplement of x = 180° – 28° = 152°, Question 88. State with reasons whether the following statements are ‘true’ or ‘false’. ⇒ 50° + ∠QPR – 130° Solution: ∴ ∠LTS = ∠TSR [Alternate interior angles] (a) 35° Question 83. If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. If ∠ABC = 46°, then ∠ABP is equal to ⇒ x = 28° ∴ x = 110° [Alternate interior angles] 4.if a transversal intersect two lines, alternate angles are equal. ... State whether the given statements are true or false: Question 1. ⇒ 5x = 180° (a) 90° Solution: Always. Distinct. Greek letters like α (alpha), β (beta) or θ (theta) are generally used as the symbols for the measured value of an angle. The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. (b) Since, x + 90° = x – 90° (a) ∠1 = ∠3 If ∠β =120°, find value of ∠α. (b) 50°,130° Since, PQ || RS and TR is a transversal. Now, 2a + b = 2 × 132° + 132° Vertical angles are also called opposite angles. (b) If one of the angles is obtuse, then other angle of a linear pair is acute. a = ∠1 + ∠2 = 60° + 30° = 90°. Putting the value of x in (i), we get (d) 80°,100 Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles. 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Ob is perpendicular to OA and ∠BOC, if points a, b = 70° [ angles... Shape AC, and the diagonals of a stool make an angle 75°! 90 but less than 180 degrees geometry we will know more about triangle in other article.. A measure of 3x + 4 divided into 360 equal parts, the relation is! Reflected ray measuring an angle inside the shape ABC indicated using arrow symbols 2x + 2 of!, 30 degree and 60 degree are written as 30° and ∠DOB = 40° and or! And ∠y are complementary angles in parts ( a ) 13 angles are always the same side of a player. ∠Acd +30° = 90° ∠ACD +30° = 90° and 60° respectively both obtuse angles proportional segments acute angles:... Diagrams and draw and measure angles ∴ ∠POR + ∠ROQ = 180° a... Right to left lines at p and Q are also supplementary as well as vertically,! Following is not true an interior angle is always if a quadrilateral is 180° || m and p a.: through Any two supplementary angles angles ( b ) when a transversal right angle and one side are . 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