question_answer

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

Answer:

Let ABCD be a parallelogram such that adjacent angles are equal.

\[\angle A\text{ }=\angle B\]

Since, \[\angle A+\angle B=180{}^\circ \]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,2\angle A=180{}^\circ \]

\[\therefore \,\,\,\,\,\,\,\,\angle A\text{ }=\angle B=\frac{180{}^\circ }{2}=90{}^\circ \]

Since, opposite angles of a parallelogram are equal.

\[\therefore \,\,\,\,\,\,\,\,\,\angle A=\angle C=90{}^\circ \,\]

and      \[\angle B=\angle D=90{}^\circ \]

Thus, \[\angle A=\text{ }90{}^\circ ,\angle B=90{}^\circ ,\]

\[\angle C=90{}^\circ \]and\[\angle D=90{}^\circ ~\]