Question

Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.

Answer 1

\[\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi\]
Number of sides in the pentagon = 5
\[ \therefore \text{ Sum of the interior angles of the pentagon }= \left( 5 - 2 \right)\pi = 3\pi\]
\[\text{ Each angle of the pentagon }= \frac{\text{Sum of the interior angles of the polygon}}{\text{Number of sides}} = \frac{3\pi}{5}\text{ rad }\]
\[\text{ Each angle of the pentagon }= \left( \frac{3\pi}{5} \times \frac{180}{\pi} \right)^\circ= 108^\circ\]