Question

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

Answer 1

Let us assume $ABCD$ to be a parallelogram.

The sum of adjacent angles of a parallelogram $=180°$

$\angle A+\angle B=180°$

$$\begin{gathered} \Rightarrow 2\angle A=180° \\ \Rightarrow \angle A=90° \end{gathered}$$

Also,,

$\begin{array}{rcl}90°+\angle B& =& 180°\\ & \Rightarrow & \angle B=180°-90°=90°\\ \angle A& =& \angle C=90°\\ \angle B& =& \angle D=90°\\ & & \end{array}$

Hence, the measure of each of the angles of the parallelogram is $90°$