question_answer 19)

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

Answer:

                Let the two adjacent angles of a parallelogram be \[{{x}^{o}}\] each. Then,    \[{{x}^{o}}+{{x}^{o}}={{180}^{o}}\] |\[\because \] Sum of the two adjacent angles of a parallelogram is 180°. \[\Rightarrow \]               \[2{{x}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[{{x}^{\text{o}}}=\frac{{{180}^{\text{o}}}}{2}\] \[\Rightarrow \]               \[{{x}^{o}}={{90}^{o}}.\] Since, the opposite angles of a parallelogram are of equal measure, therefore the measure of each of the angles of the parallelogram is \[{{90}^{o}}\], i.e., each angle of the parallelogram is a right angle.