Question

The measure of two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each angle of the parallelogram.

Answer 1

Let $\angle A$ and $\angle B$ are two adjacent angles.
But we know that sum of adjacent angles of a parallelogram is ${180}^o$
$\angle A+\angle B={180}^o$
Given that adjacent angles of a parallelogram are in the ratio $4:5$ and let that ratio be multiple of $x$
$\angle A+\angle B={180}^o$
$4x+5x={180}^o$
$9x={180}^o$
$x=180/9$
$x={20}^o$
$\angle A=4x=4\times 20={80}^o$
$\angle B=5x=5\times 20={100}^o$
Also $\angle B+\angle C={180}^o$ [Since $\angle B$ and
$\angle C$ are adjacent angles]
${100}^o+\angle C={180}^o$
$\angle C={180}^o-{100}^o={80}^o$Now, $\angle C+\angle D={180}^o$ [Since $\angle C$ and
$\angle D$ are adjacent angles]
${80}^o+\angle D={180}^o$
$\angle D={180}^o-{80}^o={100}^o$