Question

Two opposite angles of a parallelogram are ${(3x-2)}^{\circ }$ and ${(50-x)}^{\circ }$.find the measure of each angle of the parallelogram.

Answer 1

Given two opposite angles of a parallelogram are ${(3x-2)}^{\circ }$ and ${(50-x)}^{\circ }$

We know that opposite angles of a parallelogram are equal.

Hence $(3x-2)=(50-x)$

$\Rightarrow 3x+x=50+2$

$\Rightarrow 4x=52$

$\therefore x=\frac{52}{4}=13$

$(3x-2{)}^{\circ }={[3\left(13\right)-2]}^{\circ }={[39-2]}^{\circ }={37}^{\circ }$

Sum of adjacent angles is ${180}^{\circ }$

Hence other two equal opposite angles $={180}^{\circ }-{37}^{\circ }={143}^{\circ }$