Question

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5. Find the measure of each exterior angle of a regular polygon with the following number of
sides:
a. 8 sides
b. 12 sides
​

Answer 1

Answer:

Since the regular polygon has 12 sides, there will be 12 isosceles triangles at the center of the circle circumscribing the polygon. Each of these angles at the center will be 360/12 or 30 degrees. The other two angles will be

(180 - 30)/2 = 150/2 = 75 degrees. The exterior angle will be an angle of 180 - 75 -75 or 30 degrees.

Another method: There are 12 exterior angles to the figure. The sum of these 12 angles = 360 degrees, hence each angle is 30 degrees.

The sum of the interior angles = (2n - 4) right angles where n = no, of sides.

So we have a total of (2*12 - 4)right angles = (24 - 4) right angles = 20 right angles = 1800 degrees. Each interior angle = 1800/12 = 150 degrees. The exterior angle will supplementary angle of 150 degrees or 30 degrees.

Step-by-step explanation:

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