Question

The sum of opposite angles of a parallelogram is ${160}^{\circ }$ find the measure of the angles in parallelogram.

Answer 1

Let $ABCD$ is a parallelogram.

Let $\angle A+\angle C={160}^o$

We know that, opposite angles of parallelogram are equal

$\therefore$ $\angle A+\angle A={160}^o$

$\Rightarrow$ $2\angle A={160}^o$

$\Rightarrow$ $\angle A={80}^o$

$\Rightarrow$ $\angle A+\angle D={180}^o$ [ Sum of adjacent angles are ${180}^o$ in parallelogram ]

$\Rightarrow$ ${80}^o+\angle D={180}^o$

$\Rightarrow$ $\angle D={100}^o$

$\therefore$ $\angle D=\angle B={100}^o$ [Opposite angles of parallelogram are equal ]