Question

In a ||gm ABCD, if $\angle A=(2x+25{)}^{\circ }$ and $\angle B=(3x-5{)}^{\circ }$, find the value of x and the measure of each angle of the parallelogram.

Answer 1

ABCD is a parallelogram.

i.e., $\angle A=\angle Cand\angle B=\angle D$ (Opposite angles)
Also, $\angle A+\angle B={180}^0$ (Adjacent angles are supplementary) ​

$\therefore (2x+25{)}^0+(3x-5{)}^0={180}^0$
$\to 5x+20={180}^0$
$\to 5x={160}^0$
$\to x={32}^0$
$\therefore \angle A=2\times 32+25=89oand\angle B=3\times 32-5={91}^0$
Hence, $x={32}^0,\angle A=\angle C={89}^{0}and\angle B=\angle D={91}^0$