Question

The sum of two opposite angles of a parallelogram is ${130}^{\circ }$. Find the measure of each of its angles.

Answer 1

In || gm ABCD, $\angle Aand\angle C$ are opposite angles.

$\therefore \angle A+\angle C={130}^{\circ }$

$But\angle A=\angle C\left(Oppositeangles\right)\therefore \angle A=\angle C=\frac{{130}^{\circ }}{2}={65}^{\circ }But\angle A+\angle B={180}^{\circ }\left(\text{Sum of adjacent angles}\right)\Rightarrow {65}^{\circ }+\angle B={180}^{\circ }\Rightarrow \angle B={180}^{\circ }-{65}^{\circ }={115}^{\circ }But\angle D=\angle B\left(oppositeangles\right)\therefore \angle D={115}^{\circ }Hence\angle A={65}^{\circ },\angle B={115}^{\circ },\angle c={65}^{\circ }and\angle D={115}^{\circ }$