Find the angles of the parallelogram ABCD, if : (i) ∠A : ∠B = 2 : 7 (ii) ∠C = ∠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 = ⇒ 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 = ⇒ 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°.

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Mathematics

Find the angles of the parallelogram ABCD, if : (i) ∠A : ∠B = 2 : 7 (ii) ∠C = ∠D

Rectilinear Figures

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