Question 622303: Find the number of sides of the regular polygon when the measure of an exterior angle is given.
1. 30°
2. 10°
3. 24°
4. 45°
Please answer my question immediately. Thanks in advance! ;)
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! hi, there--
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The sum of the measures of the exterior angles of a polygon, one at each vertex, is always 360°.
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When you have a regular polygon, all the exterior angles have the same measure, as long as you measure corresponding angles at each vertex. So,
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[the angle measure in degrees] = [360 degrees] / [the number of vertices in the polygon]
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the number of vertices equals the number of sides, so
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[angle measure in degrees] = [360 degrees] / [the number of sides in the polygon]
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Let n be the number of sides.
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Then the angle measure is 360/n.
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I'll do the first one. You can use my example to continue.
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Feel free to email if you get stuck.
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PROBLEM 1:
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We know the angle measure is 30 degrees. We want to know the number of sides of the regular polygon.
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30 = 360/n
n = 360/30
n = 12
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The polygon has 12 sides.
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Good luck!
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Ms.Figgy
math.in.the.vortex@gmail.com
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