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Question

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

A
30°
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B
60°
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C
90°
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D
120°
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Solution

The correct option is C 90°

Let ABCD be a parallelogram as shown in the figure.

BAD=x (Assumption)
Given the adjacent angles of a parallelogram are equal.

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

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

Now,
x+x+x+x=360
(Angle sum property)

4x=360
x=3604=90
x=90

Measure of each angle is 90°.

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