Question

$\square ABCD$ is a parallelogram. The ratio of $\angle A$ and $\angle B$ of this parallelogram is $5:4$. Find the measure of $\angle B$.

Answer 1

Let the common multiple of the given ratio then

$\therefore \angle A=5x^{\circ }and\angle B=4x^{\circ }$

$\square$ ABCD is a parallelogram.

$\therefore \angle A+\angle B={180}^{\circ }$ [Adjacent angle of parallelogram are supplementary]

$\therefore 5x+4x={180}^{\circ }$

$\Rightarrow 9x={180}^{\circ }$

$\Rightarrow x=180/9$

$\Rightarrow x={20}^{\circ }$

$\angle B=4x=4\times {20}^{\circ }={80}^{\circ }$

The measure of $\angle B$ is ${80}^{\circ }$