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(d) ∠a = ∠b [Vertically opposite angles] (e) Since, POQ is a straight line. ∠EPQ+ ∠GQP = 130° + 50° = 180° ∴ ∠AOD + ∠AOC = 180° [Linear pair] ∴ The bigger angle is 2x = 2 × 60° = 120°. Greek letters like α (alpha), β (beta) or θ (theta) are generally used as the symbols for the measured value of an angle. Thus, 30 degree and 60 degree are written as 30° and 60° respectively. We know that the sum of the measures of the complementary angles is 90° 2x + 2x + 2 = 90° \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) Solution: ⇒ 2x = 166° Sometimes. Question 89. Vertical angles are also called opposite angles. The two vertically opposite angles are equal. (c) 70°, 110° As one angle is 45°, the other angle = 90-45= 45°, 2. Now, p || q and n is a transversal. What is the sum of the pairs of opposite angles? From (i) and (ii), we have (c) Since, PQ || RS and line 1 is a transversal. If two angles have a common vertex and their arms form opposite rays (see figure). \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. An angle is a figure formed by two rays meeting at a common point. ⇒ ∠2 = 180° – 135° = 45° ⇒ 9y = 180° The magnitude of the angle is the amount of rotation of one arm about the vertex to reach to the position of the second arm. Two angles forming a _________ pair are supplementary. Solution: Two lines AB and CD intersect at O (see figure). (c) (108 – b)° If the sum of measures of two angles is 90%, then the angles are _________ As if both adjacent angles are acute angles, then they do not form a linear pair. Solution: x + 61° = 180° [Linear pair] (d) Since, sum of the angles about a point is 360° = 264° + 132° = 396°. ⇒ 130° + y = 180° ∠d = ∠c [Vertically opposite angles] False And we know that vertically opposite angles are equal. (c) 36° Thus, one angle is 100° and other is 80°. In the diagram below the two angles α (alpha), and β (beta) are vertical angles and α = β. ⇒ ∠1 = 70° [Using (ii)] 2.the supplement of an obtuse angle is always acute. If the sum of measures of two angles is 180° then they are _________ The two angles are supplementary angles. (d) vertically opposite angles Now, AB || CD and ED is a transversal. According to question, Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent. (v) Every square is a rhombus. Solution: (c) Since, AB || CD and PR is a transversal (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. Answer: a = 140° , b = 40° and c = 140° . 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. Solution: (i) False (ii) True (iii) True (iv) False (v) True (vi) True (vii) True 12. \(\Rightarrow b=\frac{100^{\circ}}{5}=20^{\circ}\). ⇒ 60° – ∠L ——— (i) \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) Question 75. Therefore, B will be less than 45°. (c) ∠5 = ∠8 ∴ 6a = 120° [Corresponding 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. From (i), Its complementary angle will be _________ (d) 10° ⇒ 2∠ABP = 180° – 46° = 134 ∠AOD, ∠COB and ∠AOC, ∠BOD. (a) supplementary A road crosses a railway line at an angle of 30° as shown in figure. ∴ ∠POQ + ∠QOR = 180° [Linear pair] 2x = 180° + 20° = 200° (c) ∠3 + ∠8 = 180° (i) Since, PQ || UT and PT is a transversal. Solution: Solution: ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] (if a is perpendicular to b and b is perpendicular to c, then a is perpendicular to c) ... the measure of an … Vertical Angles: Theorem and Proof. ⇒ ∠2 = 70° ——— (ii) Arm, Question 47. Supplementary, Question 44. Then, Solution for Fill in the blank/s: True or false: A triangle in which two sides and an angle opposite one of them are given (SSA) always results in at least one… (c) When a transversal cuts two parallel lines, each pair of interior angles on the same side of the transversal are supplementary. ∴ Other angle is 180° – x. 2 1/4 in. ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] (ii) ∠x and ∠y are complementary angles. Question 5. ∴ x + y = 90° ———(i)     [Angles are complementary] (c) 30° ⇒ x + 4x = 720° ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] Answer. (b) If one of the angles is obtuse, then other angle of a linear pair is acute. Correct, there are 180° in the angle formed by any straight line. Question 90. Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. ⇒ ∠y = 180° – 35° = 145° Question 68. ∴ ∠1 + ∠5 = 180° [By(i)and(iii)] (d) 150° Question 7. Two angles that share the same vertex and one side are called adjacent angle. The two vertically opposite angles are always equal. ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] ∴ ∠5 = ∠8 [Alternate interior angles], Question 40. Now, ∠PQR = ∠PQU + ∠UQR (a) 35° A protractor is used to measure angle. Angle d is vertically opposite angle a; Angle f is vertically opposite angle c; Angle e is vertically opposite angle b . l || n and q is a transversal. Now, l is a straight line. Question 83. You can see that they can never share a side and be adjacent, so clearly this is false. An obtuse angle is more than 90 but less than 180 degrees. In the given figure, PO || RS, TR || QU and ∠PTR = 42°. Question 9. (c) write all the pairs of vertically opposite angles. ∴ AB and CD are not parallel lines. Solution: \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) \(\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}\), Question 17. \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) Solution: (b) When a transversal cuts two parallel lines, each pair of alternate interior angles are equal. According to question, (b) ∠2 + ∠5 =180° (iv) Let the angle between c and fig ∠4. Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. 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. Complementary, Question 43. Recognize that vertically opposite angle are equal. (b) 11° Vertically opposite angles are always (a) supplementary (b) complementary (c) adjacent (d) equal 33. Solution: ⇒ x = 180° – 66° = 114° Thus the required angles are 90° each. Adding (i) and (ii), we get Angle e is vertically opposite angle b . (c) 55° A full rotation consists of four right angles. Vertically opposite angles Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. (d) 45°, 45° ∴ ∠QRT = ∠RQU [Alternate interior angles] ∴ ∠1 + ∠z = 180° (Co-interior angles) Let x = 3k and y – 2k True False: Q 2: Any two right angles are supplementary. A linear pair may have two acute angles. = 35° + 55° [Using (6) & (ii)] ⇒ y = 90° – 60° = 30° True or False. The angle which makes a linear pair with an angle of 61° is of (b) ∠d=∠c 3k + 2k = 90° ⇒ 5k = 90° (b) Since, POQ is a straight line (a) 100° (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. 3. The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. (c) 85° Vertically opposite angles form a linear pair. Vertical angles are always congruent angles, so when someone asks the following question, you already know the answer. Question 20. (a) 130° You will understand this more clearly with the help of the figure given below: As if both angles are 89° and 89°, even then they cannot make the sum 180°. The opposite angles of a parallelogram are supplementary. Its complementary angle must be less than 45°. (d) Vertically opposite angles are always equal. They could be complementary in a highly skewed parallelogram in which one angle is 45 degrees. In each of the following figures, write, if any, (d) both p and q are false 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. Solution: Measures (in degrees) of two supplementary angles are consecutive odd integers. Vertically opposite angles are equal. (b) 50°,130° All Rights Reserved. (b) 4th player has the greatest kicking angle. The angles in a complete turn add up to 360 degrees. Maths Help, Free Tutorials And Useful Mathematics Resources. Solution: (c) ∠6 = ∠7 Find the value of a + b. ⇒ a = 180° – 65° = 48° [Using (i)] (b) Let the angle be x. If angle with measure x and y form a complementary ... answer as true or false. Answer: True 2.Two lines in a plane always intersect in a point. ⇒ ∠BOC + ∠COA = 90° (d) 20° Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° Adding (i) and (ii), we get ∠POR + 5 ∠POR = 90° False (a) 126° ∴ (∠2+42°) + ∠3 = 180° [Co-interior angles] (d) 64° Find ∠EFD. ⇒ ∠b = 180° – 30° = 150° [Using (1)] (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. ∴ b = 48° ——— (i) Solution: Answer. It is denoted by °. This contradicts Proposition 16 which states that an exterior angle of a triangle is always greater than the opposite interior angles. ⇒ x = 180° – 61° = 119° ⇒ 85° + a = 180° [Using (ii)] Solution: These angles are on the same side of transversal CD. Since, PQ || RS and TR is a transversal. (b) Two angles are said to be supplementary, if their sum is 180°. Question 6: Solution: ⇒ 50° = a Also, m || n and p is transversal. ∴These angles are supplementary. ANSWERS. ∴ ∠APR = ∠PRD [Alternate interior angles] The Exterior Angle is the angle formed outside a geometric shape between a side of a shape and the extended line of another side. 3d6e7434-38ca-46fb-972a-970f16a423e7 by elimu used under CC_BY-SA ; 6e8210de-7c3f-43b0-97d9-eef041bf8c3f by elimu used … The legs of a stool make an angle of 35″ with the floor as shown in figure. (b) 4 types of angles are formed i.e., vertically opposite angles, adjacent angles, supplementary angles and linear pairs. ∠AOD = ∠BOC ∠COA = ∠DOB 10. x + x = 166° Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles. In the given figure, a and bare (c) PQ || RS, line l is a transversal. 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. So, this player has the best kicking angle. (b) (3 – 6)° ∴ ∠c + ∠2 = 180° [Linear pair] (a) ∠TOS and ∠SQR is a pair of complementary angles. ∴ 4c = 120°      [Corresponding angles] Solution: Solution: Solution: In the diagram above: ... Say whether the following statement is true or false: = ... Vertically opposite angles are equal. Solution: (c) 30°, 50° If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. (ii) AB and CD ∴ Its supplement = 180° – x Also, AB || DF and BD is a transversal. (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. The diagonals of a quadrilateral_____bisect each other. Also, LM || SR and TS is a transversal. ∴ a = 36 Question 3. 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(d) Let the angle be x. Its complement -90° – x ∴ A and bare alternate interior angles. ∴ ∠POR + ∠ROS + ∠QOS = 180° Find the values of a, b and c. One obtuse angle and one acute angle can make a pair of complementary angles. ⇒ ∠2 = 180° -60° = 120° ⇒ ∠2 = 30° ———– (ii) In one particular case, when vertical angles are right … It is also called semi-circular protractor. 2. False (b) complementary This may be also simply called angle B and written in short form as ∠B. (a) 13 angles are formed. (b) 90° A point has no shape. (a) how many angles are formed? Supplemental angles are those that, if positioned adjacent to each other, form a straight angle. This is the measurement of ∠ABC.

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