A regular polygon has interior angles that are 5 times larger than each of its exterior angles. How many sides does the polygon have?
The exterior angles of a dodecagon are
The interior angles are
We need to be able to calculate this, without having to consider the size of the exterior and interior angles of all the different polygons.
Let the size of an exterior angle be
The size of the interior angle is therefore
An exterior and interior angle are supplementary angles.
The sum of the exterior angles is 360°
Number of sides (or angles) =