Question

In the following figures, ABCD is a parallelogram.

Find the values of x and y.

Answer 1

In the figure, ABCD is a parallelogram

∠D = ∠B         ...[Since opposite angles are equal.]

6x + 3y - 8 = 7y

6x + 3y - 7y = 8

6x - 4y = 8

2(3x - 2y) = 8

3x - 2y = 4   ...(i)

∠A + ∠B = 180°

4x + 20° + 7y = 180°

4x + 7y = 160°    ...(ii)

Multiply by equation (i) × 4 and equation (ii) × 3

12x - 8y = 16
12x + 21y = 480
-      -           -     
- 29y = - 464

y = `(- 464)/(- 29)`

y = 16

Put y = 16 in equation (i)

∴ 3x - 2y = 4

⇒ 3x - 2(16) = 4

⇒ 3x - 32 = 4

⇒ 3x = 4 + 32

⇒ 3x = 36

⇒ x = `36/3`

⇒ x = 12