Question

What is the exterior angle of a regular 29-gon? (Round to 2 decimal places.)

Answer 1

`12.41°`

Explanation:

Each exterior angle of a regular polygon = `(360)/n`

(where n=the number of sides of a regular polygon).

The sum of the exterior angles of any polygon is always 360°. If it is a regular polygon (meaning all the sides are the same length and all the angles are the same angle) , you simply divide 360° by the number of sides to get the degree measure of each of the exterior angles.

In this case, `360/29 = 12.41°` per exterior angle.

Interestingly, if you know this fact, you can also calculate the interior angles of a regular polygon fairly quickly. The interior plus exterior angle equals 180°, so if you know the exterior, you can get the interior (180 - exterior angle = interior angle)

I think this is actually an easier way to achieve the interior angle, rather than the formula that is typically used:

Each interior angle of a regular polygon = `((n-2)(180))/n`

(where n=the number of sides of a regular polygon).