A regular polygon has interior angles of 168°. How many sides does it have?

##360 div 12° = 30## sides

The only number that stays the same for the angles of all polygons is that the sum of the exterior angles is 360°.

If you know the size of an exterior angle##(theta)## in a regular polygon you can find the number of sides:

##360° div theta = ##number of sides

If you know the number of sides ##(n)## you can find the size of each exterior angle of a regular polygon.

##360 div n = theta##

Interior angle ##168°" "rarr "exterior angle" = 180°-168° = 12°##

##360 div 12° = 30## sides.