Question

Measures of opposite angles of parallelogram are $(3x-2{)}^{\circ }$ and $(50-x{)}^{\circ }$. Find the measure of its other angles.

• A. $143$
• B. $153$
• C. $163$
• D. $173$

Answer 1

The correct option is A $143$

Here, $ABCD$ is a parallelogram

Let $\angle A=(3x-2{)}^o$ and $C=(50-x{)}^o$

We know that in parallelogram opposite angles are equal.

$\therefore$ $\angle A=\angle C$

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

$\Rightarrow$ $4x=52$

$\Rightarrow$ $x=13$

$\Rightarrow$ $\angle A=(3x-2{)}^o=(3\times 13-2{)}^o={37}^o$

In parallelogram sum of adjacent angles are supplementary.

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

$\Rightarrow$ ${37}^o+\angle B={180}^o$

$\therefore$ $\angle B={143}^o$

Hence other two equal opposite angles are ${143}^o$