Question

How many angles does a regular polygon have if the no of sides of a regular polygon is 24?​

Answer 1

Answer:

find the measure of each exterior angel of a regular polygon with 24 sides. The sum of the exterior angeles is 360degrees. Each of the exterior angles =360/24=15 degrees.

Answer 2

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The exterior angle is the angle you turn at a corner (vertex)when going around the polygon. After a whole turn (360 degrees you have turned n corners, changing course by 24 degrees at each corner. So, 24×n=360, and n=360÷24. A polygon with 24 vertices must have 24 sides.

OR,

Sum of interior angles is (n-2)*180 So, interior angle is (n-2)*180/n Exterior angle is 180-(n-2)*180/n = 24(n-2)*180 = 156*n, 180n - 156n = 36024n = 360, n = 15