Question

The measures of two adjacent angles of a parallelogram are in the ratio $3:2$. Find the measure of each of the angles of the parallelogram

Answer 1

Let two adjacent angles A and B of $\parallel gm$ ABCD be 3x and 2x respectively.
Since the adjacent angles of a parallelogram are supplementary.
$\angle A+\angle B={180}^o$
$\Rightarrow 3x+2x={180}^o$
$\Rightarrow 5x={180}^o$
$\Rightarrow x=\frac{{180}^o}{5}={36}^o$
$\therefore \angle 3\times {36}^o={108}^o$
and, $\angle B=2\times {36}^o={72}^o$
Since the opposite angles are equal in a parallelgram, therefore, $\angle C=\angle A={108}^o$ and $\angle D=\angle B={72}^o$
Hence, $\angle A={108}^o,\angle B={72}^o,\angle C={108}^o$ and $\angle D={72}^o$