question_answer 18)

                The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

Answer:

                Let the two adjacent angles be \[3{{x}^{o}}\] and \[2{{x}^{o}}\]. Then, \[3{{x}^{o}}+2{{x}^{o}}={{180}^{o}}\] | \[\because \] Sum of the two adjacent angles of a parallelogram is \[{{180}^{o}}\] \[\Rightarrow \]               \[5{{x}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[{{x}^{\text{o}}}=\frac{{{180}^{\text{o}}}}{5}\] \[\Rightarrow \]               \[{{x}^{\text{o}}}={{36}^{\text{o}}}\] \[\Rightarrow \]               \[3{{x}^{o}}=3\times {{36}^{\text{o}}}={{108}^{\text{o}}}\] and        \[2{{x}^{\text{o}}}=2\ \times {{36}^{\text{o}}}={{72}^{\text{o}}}\] Since, the opposite angles of a parallelogram are of equal measure, therefore the measures of the angles of the parallelogram are \[{{72}^{o}},\,{{108}^{o}},\,{{72}^{o}}\] and \[{{108}^{o}}\].