Question

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram

• A. ${90}^o$
• B. ${120}^o$
• C. ${70}^o$
• D. ${80}^o$

Answer 1

The correct option is A ${90}^o$

Let $ABCD$ be the parallelogram with $\angle A=\angle B.$

We know, sum of adjacent angles of parallelogram is ${180}^o.$

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

$\Rightarrow$ $2\angle A={180}^o$ [ Since, $\angle A=\angle B$ ]

$\Rightarrow$ $\angle A={90}^o$

$\Rightarrow$ $\angle B=\angle A={90}^o$
$\Rightarrow$ $\angle A=\angle C={90}^o$ [ Opposite angles of parallelogram ]

$\Rightarrow$ $\angle B=\angle D={90}^o$ [ Opposite angles of parallelogram ]

$\therefore$ Each angle of the parallelogram measures is ${90}^o.$