Question

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

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Solution

## 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°\left[\angle \mathrm{A}=\angle \mathrm{B}\right]\\ \angle \mathrm{A}& =& \frac{180}{2}\\ \angle \mathrm{A}& =& 90°\\ \angle \mathrm{B}& =& \angle \mathrm{A}=90°\\ \angle \mathrm{A}& =& \angle \mathrm{C}=90°\left[\mathrm{Opposite}\mathrm{angles}\mathrm{of}\mathrm{parallelogram}\right]\\ \angle \mathrm{B}& =& \angle \mathrm{D}=90°\left[\mathrm{Opposite}\mathrm{angles}\mathrm{of}\mathrm{parallelogram}\right]\end{array}$$\therefore$ Each angle of the parallelogram measures is $90°$.

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