If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is

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°

Solution:

(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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