Question

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

• A. ${108}^{\circ }$
• B. ${54}^{\circ }$
• C. ${72}^{\circ }$
• D. ${81}^{\circ }$

Answer 1

Answer: (C)

${72}^{\circ }$

Let one angle be $\angle x$
Thus, smallest angle is $\frac{2}{3}\angle x$
Now, $\frac{2}{3}\angle x+\angle x=180$

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

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

$\Rightarrow \angle x=108$
Thus, the smallest angle is $\frac{2}{3}\times 108={72}^o$