question_answer 11)

                How many sides does a regular polygon have if each of its interior angles is \[{{165}^{o}}\]?

Answer:

                \[\because \] Each interior angle \[={{165}^{o}}\] \[\therefore \] Each exterior angle \[={{180}^{o}}-{{165}^{o}}={{15}^{o}}\] | linear pair property Let the number of sides be n. Then, \[n({{15}^{o}})={{360}^{o}}\] \[\Rightarrow \]               \[n=\frac{{{360}^{\text{o}}}}{{{14}^{\text{o}}}}=24\] Hence, the number of sides is 24.