Question

In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.

Answer 1

Let ∠B = x

∠A = 3 ∠B = 3x

AD || BC

∠A + ∠B = 180°

3x + x = 180°

⇒ 4x = 180°

⇒ x = 45°

∠B = 45°

∠A = 3x = 3 x 45 = 135°

and ∠B = ∠D = 45°

opposite angles of || gm are equal.

∠A = ∠C = 135°

opposite sides of //gm are equal.

AB = CD

5x – 7 = 3x + 1

⇒ 5x – 3x = 1+7

⇒ 2x = 8

⇒ x = 4

CD = 3 x 4+1 = 13

Hence 135°, 45°, 135° and 45° ; 13