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Find the sum of the measures of the interior angles of a convex 20-gon?

User Mutttenxd
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1 Answer

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Answer:

The sum of the exterior angles must always be 360 deg.

Consider an equilateral triangle 3 * 120 = 360

For a square 4 * 90 = 360

For a pentagon 5 * 72 = 360

So for a 20-gon each interior angle = 180 - 18 = 162 with an exterior angle of 18

One must rotate 18 * 20 to get the full 360 deg so the side is back where it started

Since each interior angle = 162 deg one has

20 * 162 = 3240 deg for the sum of the interior angles

User Astariul
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