Question

If an angle of a parallelogram is two- third of its adjacent angle, find the angles of a parallelogram.

Answer 1

Let adjacent angles be $x$ and $\frac{2x}{3}$
Sum of adjacent angles of a parallelogram$={180}^{\circ }$
$\therefore x+\frac{2x}{3}={180}^{\circ }$
$\frac{3x+2x}{3}=180$
$\frac{5x}{3}=180$
$\Rightarrow x=\frac{180}{5}\times 3$
$\Rightarrow x={108}^{\circ }$
Its adjacent angle is $=\frac{2x}{3}$
$=\frac{2\times 108}{3}$
$=2\times 36$
$={72}^{\circ }$
Hence, the four angle are ${108}^{\circ },{72}^{\circ },{108}^{\circ },{72}^{\circ }$.