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

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

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

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

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

Since, opposite angles of a parallelogram are equal.

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

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

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

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