# Lines & Angles

## Exercise 2.2

Question 1: In following figures, a pair of parallel lines is intersected by a transversal. Write the name of pair of type of angles shown in each figure.

Answer: (a) Corresponding angles (b) Alternate exterior angles

Answer: (c) Corresponding angles (d) Interior angles on the same side of transversal

Answer: (e) Alternate interior angles (f) Alternate exterior angles

Question 2: In the following figures, three parallel lines are intersected by two transversals. Write the name of type of pair of angles as shown in these figures.

Question 3: In the following figures, a transversal is intersecting two parallel lines at distinct points. Find the value of x; as shown in the figure.

Answer: (e) 125° (f) 47° (g) 53°

Question 4: In the following figure, AB||CD and ∠ LnB = 90°, then find the value of x.

Answer: ∠ LnB = ∠ MoC (Pair of alternate exterior angles)

∠ MoC = 90°
Or, 21x + 6 = 90°
Or, 21x = 90° - 6 = 84°
Or, x = (84°)/(21) = 4

Question 5: In the following figure, AB||CD and ∠ LNA = 75°, then find the value of x

Answer: 11x – 2 = 75° (Pair of corresponding angles)
Or, 11x = 75° + 2 = 77°
Or, x = 77° ÷ 11 = 7°

Question 6: In the following figure AB||CD and ∠ BNO = 60°, then find the value of x.

Answer: 8x – 4 = 60° (Pair of alternate angles)
Or, 8x = 60° + 4 = 64°
Or, x = 64° ÷ 8 = 8°

Question 7: In the following figure, a pair of parallel lines is intersected by a transversal. Fin the value of x+96.

Answer: In this case, internal angles on the same side of transversal are always supplementary.
Hence, both the angles would be equal to a right angle, i.e. 90°

Question 8: In the following figure, a pair of parallel lines is intersected by a transversal. Find the value of 20x+5.

Answer: In this case, internal angles on the same side of transversal are always supplementary.

Hence, 20x + 5 + 24x – 1 = 180°
Or, 44x + 4 = 180°
Or, 44x = 180° - 4 = 176°
Or, x = 176° ÷ 44 = 4
Or, 20x + 5 = 20 xx 4 + 5 = 85°

Question 9: In the following figure, a pair of parallel lines is intersected by a transversal. Find the value of 6x.

Answer: In this case; 5x + 10 = 6x (corresponding angles are equal)

Or, 6x – 5x = 10
Or, x = 10
Or, 6x = 60°

Question 10: In the following figure, a pair of parallel lines is intersected by a transversal. Find the value of x+89.

Answer: Internal angles on one side of transversal are supplementary.

Or, x + 109 + x + 89 = 180°
Or, 2x + 198 = 180°
Or, 2x = 180° - 198 = - 18
Or, x = - 18 ÷ 2 = - 9
Hence, x + 89 = - 18 + 89 = 71°

Question 11: In the following figure, a pair of parallel lines is intersected by a transversal. Find the value of 16x-6.

Answer: Since, alternate angles are equal hence, both the angles are right angles, i.e. 90°

Question 12: In the following figure, a pair of parallel lines is intersected by a transversal. Find the values of 12x-4 and 10x+10.

Hence, 12x – 4 = 10x + 10
Or, 12x = 10x + 10 + 4
Or, 12x – 10x = 14
Or, 2x = 14
Or, x = 14 ÷ 2 = 7
Hence, 12x – 4 = 12 xx 7 – 4 = 84 – 4 = 80°

Question 13: In the following figure, a pair of parallel lines is intersected by a transversal. Find the value of x.

Answer: Alternate exterior angles are equal.

Hence, x + 112 = 105°
Or, x = 105 – 112 = - 7