What regular polygon has a exterior angle of 24 degrees?

We know that the sum of the exterior angles of a regular polygon is 360°. Since the exterior angle is 24°, then

24°n = 360° divide both sides by 24°;

n = 15

Thus a 15-sided regular polygon has an exterior angle of 24°.

If you don't remember the above fact, you can work in this way:

If the exterior angle is 24°, then the angle of polygon will be 156° (180 - 24).

Since the sum of the angle of the polygon is equal to (n - 2)180°, then we have:

156° n = (n - 2)180°

156° n = 180°n - 360° subtract 156°n and add 360° to both sides;

360° = 24°n divide by 24° to both sides;

15 = n