Question

The opposite of a parallelogram $(3x-2)$ and $(x+48)$. Find the measure of each angle at the parallelogram.

Answer 1

Let four angles of given parallelogram taken in order be $\angle A,\angle B,\angle Cand\angle D$ respectively.

Here opposite angles given$\angle A=3x+2$ and $\angle C=x+48$

We know that opposite angles of a parallelogram are equal

$\therefore 3x-2=x+48$

$\Rightarrow 2x=50$

$\Rightarrow x=50/2$

$\Rightarrow x=25$

$\therefore 3x-2=3\left(25\right)-2=75-2={73}^{\circ }$

$\angle A=\angle C={73}^{\circ }$

Also we know that sum of two adjacent angles of a parallelogram is $180^{\circ}$

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

$\Rightarrow {73}^{\circ }+\angle B={180}^{\circ }$

$\Rightarrow \angle B={180}^{\circ }-{73}^{\circ }$

$\Rightarrow \angle B={107}^{\circ }=\angle D$ (opposite angles are equal)

$\therefore$ All four angles of given parallelogram are ${73}^{\circ },{107}^{\circ },{73}^{\circ },{107}^{\circ }$.