SOLUTION: 1. How many exterior angles are there in a n-gon? Are they all considered when using the Polygon Exterior Angles Theorem? 2. Find the sum of the measures of the interior angle

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Question 140725: 1. How many exterior angles are there in a n-gon? Are they all considered when using the Polygon Exterior Angles Theorem?

2. Find the sum of the measures of the interior angles of the convex polygon.
10-Gon
15-Gon
20-Gon

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1. How many exterior angles are there in a n-gon?
Ans: n
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Are they all considered when using the Polygon Exterior Angles Theorem?
Ans: yes
Sum of exterior angles is always 360 degrees
Each exterior angle is 360/n
each interior angle is the suppliment of an exterior angle
each interior angle is 180-(360/n) = (180n-360)/n
The sum of the n interior angles is 180n-360 = 180(n-2)
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2. Find the sum of the measures of the interior angles of the convex polygon.
10-Gon: 180*8
15-Gon: 180*13
20-Gon: 180*18
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Cheers,
Stan H.