Question

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

Answer 1

$$\text{ Sum of the interior angles of the polygon }=(n-2)\pi$$
Number of sides in the duodecagon = 12 
$$\therefore \text{ Sum of the interior angles of the duodecagon }=(12-2)\pi =10\pi$$
$$\text{ Each angle of the duodecagon }=\frac{\text{ Sum of the interior angles of the polygon }}{\text{ Number of sides }}=\frac{10\pi }{12}=\frac{5\pi }{6}\text{ rad }$$
$$\text{ Each angle of duodecagon }={(\frac{5\pi }{6}\times \frac{180}{\pi })}^{\circ }={150}^{\circ }$$