A regular polygon has interior angles that are 5 times larger than each of its exterior angles. How many sides does the polygon have?

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 ##x##
The size of the interior angle is therefore ##5x##
An exterior and interior angle are supplementary angles.
##x + 5x = 180 rArr 6x = 180##
##x = 30## This is size of each exterior angle (##ext angle##)
The sum of the exterior angles is 360
Number of sides (or angles) = ##360/(ext angle)##
##360/30 = 12## sides