Question

Two adjacent angles of a parallelogram are equal. What is the measure of each of the angles?

• A. 30°
• B. 60°
• C. 90°
• D. 120°

Answer 1

The correct option is C 90°


Let ABCD be a parallelogram as shown in the figure.

$\angle BAD=x\text{(Assumption)}$
Given the adjacent angles of a parallelogram are equal.

Hence,
$\angle ADC=\angle BAD=x$
$\angle DCB=\angle BAD=x$
(Opposite angles of a parallogram are equal)

$\angle ADC=\angle CBA=x$
(Opposite angles of a parallogram are equal)

Now,
$x+x+x+x={360}^{\circ }$
(Angle sum property)

$\Rightarrow 4x={360}^{\circ }$
$\Rightarrow x=\frac{{360}^{\circ }}{4}={90}^{\circ }$
$\Rightarrow x={90}^{\circ }$

Measure of each angle is 90°.