Tick (✓) the correct answer

Question:

Tick (✓) the correct answer:

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

(a) 54°

(b) 72°

(c) 81°

(d) 108°

Solution:

(b) $72^{\circ}$

Let $x^{\circ}$ be the angle of the parallelogram.

Sum of the adjacent angles of a parallelogram is $180^{\circ}$.

$\therefore x+\left(\frac{2}{3} \times x\right)=180$

$\Rightarrow x+\frac{2 x}{3}=180$

$\Rightarrow\left(x+\frac{2 x}{3}\right)=180$

$\Rightarrow \frac{5 x}{3}=180$

$\Rightarrow x=\left(180 \times \frac{3}{5}\right)$

$\Rightarrow x=108$

Hence, one angle of the parallelogram is $108^{\circ}$.

Its adjacent angle $=(180-108)^{\circ}=72^{\circ}$

Therefore, the smallest angle of the parallelogram is $72^{\circ}$.

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