What is the measure of one interior angle of a regular convex 31gon?

Answer 1

The easiest way to calculate this is to use the facts that

• the sum of the interior and exterior angles is 180o; and
• the sum of the exterior angles of any polygon is 360o.

For a regular polygon, each exterior angle will be 360o divided by the number of sides. The interior angle is then 180o - the exterior angle.

For a 31-gon:

exterior_angle = 360° ÷ 31

= 1119/31o

⇒ interior_angle = 180° - 1119/31o

= 16812/31°

≈ 168.39o

Use the Interior Angle Formula directly

The sum of interior angles for a polygon of n sides is (n-2) x 180° and individual angles for a regular polygon will be (n-2) 180°/n

Plugging in the value n=31, we have one angle = 29(180)/31 = 168.39°