Question

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

(a) ${54}^{\circ }$ (b) ${72}^{\circ }$

(c)${81}^{\circ }$ (d) ${108}^{\circ }$

Answer 1

Let one adjacent angle $=x$

Then its adjacent angle (smallest) = $\frac{2}{3}x$

Since, in a parallelogram, sum of any two consecutive angles is ${180}^{\circ }$.

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

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

$\Rightarrow x={180}^{\circ }\times \frac{3}{5}$

$\Rightarrow x={108}^{\circ }$

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

In a parallelogram, opposite angles are equal.

i.e., The angles of parallelogram are ${108}^{\circ },{72}^{\circ },{108}^{\circ }$ and ${72}^{\circ }$

Therefore, the smallest angle $={72}^{\circ }$

Hence option B is correct.