Question 826835: Each exterior angle of a regular polygon measures 20 degrees. Determine the sum of its interior angles. Answer by jsmallt9(3758) (Show Source):
The exterior angles of a convex polygon add up to 360 degrees.
The interior and exterior angles of a regular polygon are all congruent to each other.
At each vertex, the interior angle and the exterior angle form a linear pair.
Linear pairs are always supplementary (which means the two angles add up to 180).
Since the exterior angles are all congruent they are all 20 degrees. Since they add up to 360, dividing 360 by 20 will tell us how many exterior angles there are:
So there are 18 exterior angles. This also means that there are 18 vertices and 18 interior angles.
Since each interior/exterior pair is supplementary and since the exterior angle is 20, the interior angle is 180-20 = 160 degrees.
So with 18 interior angles, each of them 160 degrees, we have:
18*160 = 2880
for the sum of all the interior angles.
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