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.

parallel lines and transversal

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


parallel lines and transversal

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

parallel lines and 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.

parallel lines and transversal

Answer: (a) Alternate interior angles

parallel lines and transversal

Answer: (b) Alternate exterior angles

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.

parallel lines and transversal

Answer: (a) 110° (b) 84°

parallel lines and transversal

Answer: (c) 80° (d) 111°

parallel lines and transversal

Answer: (e) 125° (f) 47° (g) 53°

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

parallel lines and transversal

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

parallel lines and transversal

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.

parallel lines and transversal

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`.

parallel lines and transversal

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`.

parallel lines and transversal

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.

parallel lines and transversal

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`.

parallel lines and transversal

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`.

parallel lines and transversal

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`.

parallel lines and transversal

Answer: Corresponding angles are equal.

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.

parallel lines and transversal

Answer: Alternate exterior angles are equal.

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



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