Question

In a parallelogram, if an angle be ${80}^{\circ }$ then find the remaining angles.

Answer 1

Given:

One of the angle of a parallelogram is ${80}^{\circ }$.

Let $ABCD$ be a parallelogram and $\angle A$ be ${80}^{\circ }$.

Since opposites angles are equal in a parallelogram.

$\Rightarrow \angle C=\angle A={80}^{\circ }$ ---(1)

Since, sum of any two consecutive angles of a parallelogram is ${180}^{\circ }$

$\Rightarrow \angle A+\angle B={180}^{\circ }$

$\Rightarrow {80}^{\circ }+\angle B={180}^{\circ }$

$\Rightarrow \angle B={180}^{\circ }-{80}^{\circ }$

$\Rightarrow \angle B={100}^{\circ }$ ---(2)

and, $\angle B=\angle D={100}^{\circ }$ [Since, opposite angles of a parallelogram] --(3)

$\therefore \angle A={80}^{\circ },\angle B={100}^{\circ },\angle C={80}^{\circ },\angle D={100}^{\circ }$

Therefore, the angles are ${80}^{\circ },{80}^{\circ },{100}^{\circ },{100}^{\circ }$