Question

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

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

$\Rightarrow 4x=52$

$\therefore x=13$

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

We know that,

The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary.

Another angle $={180}^{\circ }-{37}^{\circ }={143}^{\circ }$

The measure of each angle of the parallelogram.

${37}^{\circ },{143}^{\circ },{37}^{\circ },{143}^{\circ }$