question_answer 1)

Find the angle which is equal to its supplement.

Answer:

                Let the angle be \[{{x}^{o}}\]. Its supplement \[={{180}^{o}}-\text{ }{{x}^{o}}\] According to the question, \[{{x}^{o}}={{180}^{o}}-{{x}^{o}}\] \[\Rightarrow \]               \[{{x}^{o}}+{{x}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[2{{x}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[{{x}^{o}}=\frac{{{180}^{o}}}{2}={{90}^{o}}\] Hence, the required angle is \[\text{9}{{0}^{o}}\].