Question

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

• A. ${65}^{\circ }$
• B. ${55}^{\circ }$
• C. ${72}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is C

${72}^{\circ }$

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

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