**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.

**Answer:** (a) Alternate interior angles

**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.

**Answer:** (a) 110° (b) 84°

**Answer:** (c) 80° (d) 111°

**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`.

**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.

**Answer:** Alternate exterior angles are equal.

Hence, `x + 112 = 105°`

Or, `x = 105 – 112 = - 7`

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