Question

If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is
(a) 108°
(b) 54°
(c) 72°
(d) 81°

Answer 1

(c) 72°​

Explanation:
Let ABCD be a parallelogram.
∴ ∠A = ∠C and ∠B = ∠D (Opposite angles)
Let ∠A = x and ∠​B = $\frac{2}{3}x$(4x5)
∴ ∠​A + ∠B = 180^o (Adjacent angles are supplementary)
⇒ x + $\frac{2}{3}$x = 180^o
⇒ $\frac{5}{3}x=180°$
⇒ x = 108^o
∴ ∠B = $\frac{2}{3}\times$ (108^o) = 72^o
Hence, ∠A = ∠C = 108^o and ∠B = ∠D = 72^o
⇒9x5 = 180o⇒x = 100o∠A = 100o an