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Please help with 2 and 3, show work if possible!

Please help with 2 and 3, show work if possible!-example-1
User MeW
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1 Answer

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Assuming these are all regular polygons, we use the fact that the sum of all exterior angles of a regular n-gon is 360°. So each exterior angle has measure 360°/n.

These angles are supplementary to the interior angles, so each interior angle has measure 180° - 360°/n.

Since there are n such angles, the sum of the interior angle measures is

n (180° - 360°/n) = 180° n - 360° = 180° (n - 2)

like in the given formula.

2. A heptagon has 7 sides, so the sum of its interior angle measures is 180° (7 - 2) = 900°

3. A decagon has 10 sides, so the interior angle sum is 180° (10 - 2) = 1440°

User Dario Oddenino
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