Find the angles of the parallelogram ABCD, if :

(i) ∠A : ∠B = 2 : 7

(ii) ∠C = $\dfrac{2}{3}$ ∠D

(i) Given: ABCD is a parallelogram.

Let ∠A = 2a and ∠B = 7a.

In a parallelogram, the sum of adjacent angles is 180°.

⇒ ∠A + ∠B = 180°

⇒ 2a + 7a = 180°

⇒ 9a = 180°

⇒ a = $\dfrac{180°}{9}$

⇒ a = 20°

∠A = 2a = 2 x 20° = 40°

∠B = 7a = 7 x 20° = 140°

In a parallelogram, opposite angles are equal, so:

∠C = ∠A = 40°

∠D = ∠B = 140°

Hence, the angles of the parallelogram are 40°, 140°, 40° and 140°.

(ii)

∠C : ∠D = 2 : 3

Let ∠C = 2a and ∠D = 3a.

In a parallelogram, the sum of adjacent angles is 180°.

⇒ ∠C + ∠D = 180°

⇒ 2a + 3a = 180°

⇒ 5a = 180°

⇒ a = $\dfrac{180°}{5}$

⇒ a = 36°

∠A = 2a = 2 x 36° = 72°

∠B = 7a = 5 x 36° = 108°

In a parallelogram, opposite angles are equal, so:

∠A = ∠C = 72°

∠B = ∠D = 108°

Hence, the angles of the parallelogram are 72°, 108°, 72° and 108°.