Question

Find the measure of each interior angle of a regular convex dodecagon. Show equations and all work that leads to your answer.

Answer 1

The exterior angles to any convex polygon sum to 360 degrees in measure, so that for a regular dodecagon (12-gon) each exterior angle has measure

$\dfrac{360^\circ}{12}=30^\circ$

Exterior angles are complementary to interior angles, which means each interior angle has measure

$180^\circ-30^\circ=\boxed{150^\circ}$