Quest of Nine

The Book

Angles in regular polygons

You can easily calculate the internal angle of any regular polygon.

internal angle of a regular polygon

Imagine walking around the perimeter of the hexagon on the right in the direction of the red line.

When you get to the first corner you will have to turn through the angle of turn to follow the next side.

You will do this six times as you walk around the shape and then end up facing in the same direction as you did at the beginning.

You will have turned through a complete circle (360°). You turned 6 corners ~ so each angle of turn must be:

360°/6 = 60°.

Since the internal angle and the angle of turn together make a straight line (180°) then the internal angle for the hexagon will be:

180° - 60° = 120°

You can calculate the internal angle for any regular polygon in the same way ~ i.e. internal angle = 180°- angle of turn


internal angle = 180°- (360°/number of sides)

Can you work out the internal angles for the common regular polygons?