6. Solution: Solution: (ii) EF is a straight line. ⇒ 50° + ∠QPR – 130° Question 32. 90°, Question 55. \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) Solution: ∴ ∠1 = 34° [Alternate interior angles] ⇒ ∠2 = 180° – 135° = 45° Solution: Question 60. (c) 60° ⇒ ∠ABC = 180° – 120° [Using (ii)] Also, p || q and l is a transversal. 5.27, a= 40°. ⇒ (3a + 5)° + (2a-25)° = 180° We have, \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) 2 1/4 in. Vertically Opposite Angles: The vertically opposite angles formed when two lines intersect each other at a point. \(\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}\) ⇒ ∠x + ∠2 = 180° [Co-interior angles] (b) ∠4 = ∠8 ∴ y + 48° = 180° [Co-interior angles] Solution: No, two acute angles cannot form a pair of supplementary angles. (c) alternate interior angles (c) p is false and q is true The red angles ∠ JQM and ∠ LQK are equal, as are the blue angles ∠ JQL and ∠ MQK. (b) ∠d=∠c (a) 120° ∴ ∠4 = 75° [Alternate interior angles], Question 91. Its complementary angle will be _________ (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. (a) 60°, 120° Two vertically opposite angles are always equal. Now, e || f and c is a transversal. Now, a + b = 45° + 55° = 100°, Question 105. Theorem: In a pair of … (d) 150° Understanding Trigonometric Ratios With Application to Triangles – Maths Tips. true. sometimes. \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. As a linear pair has one acute angle and one obtuse angle. Question 59. 9. A pair of vertically opposite angles are always equal to each other. (a) 36° The sum of the Interior Angle and the Exterior Angle are 360°. ∴ a + b = c [Alternate interior angles] ∴ Its supplement = 180° – x Three lines AB, CD and EF intersect each other at O. Also, AB || DF and BD is a transversal. (d) 60° Question 76. ∴ ∠2 = ∠6= (34 – b)° ——– (i)[Corresponding angles] ⇒ x = 150°, Question 10. ∠a = ∠3 [Vertically opposite angles] and its supplement = 180° – x= 180°- 100 = 80° Here they are adjacent angles also. 2. true or false: planes are created by 3 collinear points. In the given figure, PO || RS, TR || QU and ∠PTR = 42°. Question 4: Look at the figure below. So, this player has the best kicking angle. If an angle is 60° less than two times of its supplement, then the greater angle is (a) 100° (b) 80° (c) 60° (d) 120° 35. Statements a and bare as given below: (c) write all the pairs of vertically opposite angles. Thus, m || n as the sum of co-interior angles is 180°. (c) 72° Sources. So, this player has the best kicking angle. ∴ a + b = c [Alternate interior angles], Question 106. Solution: The two vertically opposite angles are always equal. ⇒ 100° + a = 180° Solution: Now, e || f and d is a transversal. It is also called semi-circular protractor. If ∠POR = 90° and x : y = 3 : 2, then z is equal to Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] Draw a straight line. In figure, OB is perpendicular to OA and ∠BOC = 49°. Solution: How many degrees are in a “straight angle”? Greek letters like α (alpha), β (beta) or θ (theta) are generally used as the symbols for the measured value of an angle. alternate Interior angles are on the _________ side of the transversal. The following angles are also complementary as the sum of their measures is equal 90 degrees, Two angles whose measures add to 180 degrees are called Supplementary Angles. (a) alternate exterior angles Can two obtuse angles form a … True False: Q 5: If two lines are perpendicular to each other, then all the pairs of vertically opposite angles formed are supplementary. Question 57. The value of bis (a) 20° (b) 24° (c) 36° (d) 120° 34. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) (d) 80° According to question, (a) If one of the angles is acute, then other angle of a linear pair is obtuse. Solution: Question 45. (d) Since, x – 10° + 190°- x = 180° 60°: Let the angle be x. (c) complementary Answer: True 2.Two lines in a plane always intersect in a point. 4. Then, As two acute angles can make a pair of complementary angles. (c) 20°, 50° \(\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}\), Question 17. Now, ∠BOC = (x + 5)° = (35 + 5) = 40° Name; The origin is at the centre. (c) 30°, 50° (v) Every square is a rhombus. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° An angle is generally named by three consecutive alphabets such as A, B and C or X, Y and Z. Solution: Solution: In the given figure, if l || m, find the values of a and b. ⇒ ∠2 = 30° ———– (ii) True, Question 64. An angle is 45°. (∵ 45° + 45° = 90° and 60° + 30°= 90°). ∠2 = ∠3 [Alternate interior angles] Filed Under: Geometry Tagged With: acute angle, Adjacent Angle, angle, complementary angle, Complete Angle, Exterior Angle, Interior Angle, obtuse angle, Reflex Angle, right angle, Straight Angle, supplementary angle, Vertically opposite angle, […] Complement angles add up to 90°. 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Solution: Two lines AB and CD intersect at O (see figure). Now, LM || QP and QT is a transversal. As one angle is 45°, the other angle = 90-45= 45°, 2. (b) 100° Answer. and b = 132° [Vertically opposite angles] In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. An angle is a figure formed by two rays meeting at a common point. (a) 100° ∠FOR + ∠QRH = 123° + 57° = 180° (b) p is true and q is false (iii) Let the angle between d and fis ∠3. (a) ∠1 = ∠5 Now, a + b = 180° [Angles on a straight line PQ] (vii) The diagonals of a trapezium, divide each other into proportional segments. 45° : Given, angle = 45° (b) 45° (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. (d) (ii) is false ⇒ 90° + x + y = 180° Give reason. False Solution: True, Question 62. As vertically opposite angles are always equal but do not form a linear pair. ∴ a = 36 (c) If one of the angles is right, then other angle of a linear pair is also right. x = 2(180° – x) – 60° (d) We have, Since, l || m and p is a transversal. (c) ∠6 = ∠7 Directions: In questions 42 to 56, fill in the blanks to make the statements true. The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. If the complement of an angle is 62°, then find its supplement. Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] Now, EF || GH and AB is a transversal. ⇒ 5b – 180° – 80° = 100° (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. Solution: (d) 45°, 45° 1. Answer: a = 140°, b = 40° and c = 140°. (b) 30° ⇒ 3x = 300° When measuring an angle, the centre of the protractor is placed over the vertex (corner) B of the angle and the base line of the protractor is placed along one of the lines of the angle BC. Instead, they create CONGRUENT veritcal angles. In the above example of clock, the two hands initially make smallest angle 0° and on one complete rotation by the minute hand, the two hands make maximum angle and is named as the angle 360 degree or 360°. ∴ ∠SPQ = ∠PQU [Alternate interior angles] If a quadrilateral has three angles of equal measure, then the fourth angle must be a right angle. Also, a || d and f is a transversal. (d) 75° Then, angles a and bare respectively Solution: Question 2. \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) but ∠4 ≠ ∠8, Question 38. ⇒ ∠QPR = 130° – 50° = 80°, Question 11. \(\Rightarrow \quad x=\frac{210}{6}=35\) ⇒ ∠c = 180° – 30° = 150° An obtuse angle is more than 90 but less than 180 degrees. Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. ∴ The angles between North and West and South and East are supplementary. ⇒ x = 360° – 2x – 60° true or false 1.vertically opposite angles are always supplementary. (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. \(\Rightarrow \angle A B P=\frac{134^{\circ}}{2}=67^{\circ}\). ⇒ 130° = b Find the angles x and y. Help Amisha in finding the angles. Two adjacent angles always form a linear pair. Question 77. Hence α + β= 180 degree, Now, p || q and m is a transversal. Solution: (c) one of its angles is right? Then, which one of the following is not true? ⇒ x + 2x = 300° ⇒ 3a – b = 180 – 2a – b Now, ∠2-(3a – b)° [From (i)] ∴ 6y + y + 2y = 180° (a) (2 + b)° Question 3: Look at the figure below. When two lines intersect each other at one point and the angles opposite to each other are formed with the help of that two intersected lines, then the angles are called vertically opposite angles. The sum of the Interior Angle and the Exterior Angle are 180°. Question 7. Solution: Two angles are vertical. (b): Since, vertically opposite angles are equal. Also, RQ || TS and RS is a transversal. Any angle can have adjacent angles on its both sides. Also, m || n and QR is a transversal. (c) (i) is false but (ii) and (iii) are true \(\Rightarrow \quad a=\frac{120^{\circ}}{6}=20^{\circ}\) Solution: Solution: ANSWERS. The angle measures the amount of turn between the two arms two and is usually measured in degrees or radians. Solution: Angles which are both supplementary and vertically opposite are Question 103. ∴ x + 64° + 46° +100° – 360° Question 78. (c) Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other. ⇒ 130° + y = 180° Question 30. \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) Question 67. ∴ ∠2 + 3 = 180° [Co-interior angles] = 60° Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. (c) 16° For this example, I suggest a horizontal line. Thus, the required angles are 60° and 30°. If ∠β =120°, find value of ∠α. (b) two pairs of supplementary angles. (a) 30° ⇒ 50° + ∠BCD = 180° ⇒ 42° + ∠QUR = 180° [Using (i)] ∴ b = 50° [Alternate interior angles]. Two complementary angles are not necessarily adjacent angles, Two adjacent angles are always supplementary, The two vertically opposite angles cannot be adjacent angles. ∴ AOB is a straight line. Think of the two hands of a clock at 12 o’clock. Solution: (b) 67° In the given figure, two parallel lines l and m are cut by two transversals p and 4. Solution: Find the angles. (b) 90° ⇒ a = 180° – 65° = 48° [Using (i)] Now, PQ || RT and RQ is a transversal. Find the values of a, b and c. In the given figure, PO || RS. (b) supplementary ∴ Angles between South and West and South and East are making a linear pair. (c) 110° (ii) There is no pair of vertically opposite angles. The sum of the linear pair of angles is always equal to 180 degrees. (a) Since, POQ is a straight line. If two angles have a common vertex and their arms form opposite rays (see figure). In Geometry we will learn more about the angles with magnitudes between 0 and 360°. Now, SOT is a straight line (b) 125° 2. Question 5. The Exterior Angle is the angle formed outside a geometric shape between a side of a shape and the extended line of another side. ⇒ ∠QUR = 180° – 42° = 138°. ∴These angles are supplementary. Solution: (d) 60° An angle that is less than 90 degrees is called an acute angle. Definition and properties of vertical (or opposite) angles. ∴ ∠1 + ∠z = 180° (Co-interior angles) 3. (c) ∠a + ∠d = 180° Measures (in degrees) of two complementary angles are two consecutive even integers. Two angles making a linear pair are always supplementary. Solution: It is a right angle and measures 90°, Question 2: Look at the figure below and find ∠ACD, ∠ACB is a right angle Tags: Question 15 . ∴ b + 132° = 180° [Co-interior angles] (a) 36° (d) 62° ∴ ∠1 + ∠x = 180° [Co-interior angles] ⇒ x + x = 180° [∵Angles are supplementary] Now, l || m and n is a transversal. ∴ ∠1 = ∠3 [Corresponding angles] Solution: Which angles are corresponding angles? ⇒ x = 28° ⇒ d = 180°- 38° = 142° [Using (i)] Which player has the best the greatest) kicking angle? (d) equal ∵ AB is a straight line. Solution: Solution: Solution: Since, l || m and is a transversal. Solution: Find the values of a, b and c. Putting value of x in (i), we get When the sum of the measures of two angles is 90°, the angles are called (а) supplementary angles (b) complementary angles (c) adjacent angles (d) vertically opposite angles. Two lines will meet in one point only when they are parallel. Question 25. Solution: 2x + 1 + 2x + 3 = 180° ⇒ 90° – 62° = x (i) Name all the pairs of adjacent angles. Alternate exterior Angles. 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. ∴ ∠5 = ∠8 [Alternate interior angles], Question 40. It is denoted by ∠θ. Solution: (c) four pairs of adjacent angles. (ii) EF || GH ∴ x + 2x = 180° Solution: Since, AF || ED and FD is a transversal. (ii) d and e (a) Since, PQ || SR and RP is a transversal ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 Vertically opposite angles form a linear pair. in a plane, the relation "is perpendicular to" is transitive. Now, CD is a straight line. If x= 30°, then ∠QOR is Thus, ∠EFD = 70°, Question 93. Hence ∠ACD = 60°. Euclid's Proposition 28 extends this result in two ways. Are Vertical Angles Adjacent? (b) When a transversal cuts two parallel lines, each pair of alternate interior angles are equal. In the figure below α + β= 180 degree, angles α and β are Supplementary Angles. Then, (ii) ∠x and ∠y are complementary angles. This gives a measure of the angle. ∴ x + y = 180° ———– (i) (a) 13 angles are formed. (b) 4th player has the greatest kicking angle. Find the reflex ∠EFG. ∴ AB || CD. ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. (a) 130° ∴ a = f [Corresponding angles] We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. (c) 5° Find the values of a and b. False. True, Question 63. Question 86. ⇒ x + 4x = 720° Question 28. Question 79. (d) 22.5° Which of the following statements is false? Supplementary, Question 44. In the given figure, lines PQ and ST intersect at O. Question 83. ... the bisectors of vertical angles are opposite rays. In Fig. Therefore, a complement of an angle say, h, is 90° – h. […], Your email address will not be published. ∴ Let each angle be x. Since, PQ || RT and PR is a transversal. ⇒ ∠CDE-120° ——- (ii) [Using (1)] (b) Let the angle be x. Two angles that share the same vertex and one side are called adjacent angle. If ∠ABC = 46°, then ∠ABP is equal to Two lines in a plane which do not meet at a point anywhere are called _________ lines. (See blue line). Given points A, O and B are collinear. Vertical Angles are a pair of nonadjacent anglesopposite each other formed when two lines cross.Vertical angles are two angles opposite of each other. (c) When a transversal cuts two parallel lines, each pair of interior angles on the same side of the transversal are supplementary. Solution: Find ∠ABC and ∠CDE. Now, QP || RS and PR is a transversal. (iv) Let the angle between c and fig ∠4. ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 Now, CD and EF intersect each other at O. Correct, there are 180° in the angle formed by any straight line. ⇒ ∠3 – 180° – 105° = 75° [From (ii) part] ∴ Let a = 3x and b – 2x Question 90. The diagram below shows a protractor. (a) pair of complementary angles Vertically opposite angles are either both acute angles or both obtuse angles. Magnitudes between 0 and 360° Maths Solutions Chapter 5 lines and a is transversal pair of nonadjacent anglesopposite other. By ∠ABC ∠PTR – ∠TRU= 42° ——— ( i ) [ Alternate interior angles ] Now, CH DF. May help to trace the diagrams and draw and measure angles a complementary... answer as true False! Supplementary ( b ) Now the players are lined up in a complete turn add up to degrees... Know the answer so clearly this is angle at vertex b two players are practicing their kicks ;... 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