Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let an angle of parallelogram be 'x '
and its adjacent angle be $\frac{2}{3}\times x$
$x+\frac{2}{3}\times x={180}^{\circ }$ [ $\because$Adjacent angles of a parallelogram are supplementary]
$\Rightarrow \frac{5}{3}\times x={180}^{\circ }$
$x=\frac{{180}^{\circ }\times 3}{5}={108}^{\circ }$
$\therefore$ Smallest angle $=\frac{2}{3}\times x=\frac{2}{3}\times {108}^{\circ }={72}^{\circ }$