Question

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

Answer 1

Find the measure of each angle of the parallelogram.

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

The sum of adjacent angles of a parallelogram is$180°$.

$\begin{array}{rcl}\angle \mathrm{A}+\angle \mathrm{B}& =& 180°\\ 2\angle \mathrm{A}& =& 180°[\angle \mathrm{A}=\angle \mathrm{B}]\\ \angle \mathrm{A}& =& \frac{180}{2}\\ \angle \mathrm{A}& =& 90°\\ \angle \mathrm{B}& =& \angle \mathrm{A}=90°\\ \angle \mathrm{A}& =& \angle \mathrm{C}=90°[\mathrm{Opposite}\mathrm{angles}\mathrm{of}\mathrm{parallelogram}]\\ \angle \mathrm{B}& =& \angle \mathrm{D}=90°[\mathrm{Opposite}\mathrm{angles}\mathrm{of}\mathrm{parallelogram}]\end{array}$

$\therefore$ Each angle of the parallelogram measures is $90°$.