If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is
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°
(c) 72°
Explanation:
Let ABCD be a parallelogram.
∴ ∠A = ∠C and ∠B = ∠D (Opposite angles)
Let $\angle A=x$ and $\angle B=\frac{2}{3} x$
$\therefore \angle A+\angle B=180^{\circ}$ (Adjacent angles are supplementary)
$\Rightarrow x+\frac{2}{3} x=180^{\circ}$
$\Rightarrow \frac{5}{3} x=180^{\circ}$
$\Rightarrow x=108^{\circ}$
$\therefore \angle B=\frac{2}{3} \times\left(108^{\circ}\right)=72^{\circ}$
Hence, $\angle A=\angle C=108^{\circ}$ and $\angle B=\angle D=72^{\circ}$
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