Question

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

Answer 1

\[\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi\]
Number of sides in the heptagon = 7 
\[ \therefore\text{ Sum of the interior angles of the heptagon }= \left( 7 - 2 \right)\pi = 5\pi\]
\[\text{ Each angle of the heptagon }= \frac{\text{ Sum of the interior angles of the polygon}}{\text{ Number of sides}} = \frac{5\pi}{7}\text{ rad }\]
\[\text{Each angle of the heptagon }= \left( \frac{5\pi}{7} \times \frac{180}{\pi} \right)^\circ= \left( \frac{900}{7} \right)^\circ= 128^\circ 34'17 '' \]