Question

ABCDE is a pentagon in which AB is parallel to DC and ∠A : ∠E : ∠D = 1 : 2 : 3. Find angle A.

Answer 1

Given AB || DC
⇒ ∠B + ∠C = 180°
Also,
∠A : ∠E : ∠D = 1 : 2 : 3
⇒ ∠A = x, ∠E = 2x and ∠D = 3x
Since,
∠A + ∠B + ∠C + ∠D + ∠E = (5 - 2) x 180°
⇒ ∠A + (∠B + ∠C) + ∠D + ∠E = 3 x 180°
⇒ x + 180° + 3x + 2x = 540°
⇒ 6x + 180° = 540°
⇒ 6x = 360°
⇒ x = 60°
Hence,
∠A = 60°.