Question

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

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

Answer 1

The correct option is C

${72}^{\circ }$

Let adjacent angle of the || gm = x

Then secong angle $=\frac{2}{3}x$

$\therefore x+\frac{2}{3}x={180}^{\circ }$ (Sum of two adjacent angles of a || gm is ${180}^{\circ }$)

$\Rightarrow \frac{5}{3}x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }\times 3}{5}=36\times 3={108}^{\circ }$

$\therefore Smallerangle=\frac{2}{3}\times {108}^{\circ }$

$=2\times 36={72}^{\circ }$