Write a proof of the Polygon Interior Angle-Sum Theorem.

The sum of the measures of the interior angles of a convex n-gon is 180 times (n-2).

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into how many triangles?

Question

Mathematics

Valeria Herman

11 July, 22:34

Write a proof of the Polygon Interior Angle-Sum Theorem.

The sum of the measures of the interior angles of a convex n-gon is 180 times (n-2).

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into how many triangles?

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Answers (1)

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Natalia Juarez · Answer 1

You can always decompose a polygon into n-2 triangles, of which each is a triangle. The sum of the angles in a triangle is 180, so you get the formula 180 (n-2).

The n-sided polygon can always be decomposed into n-2 triangles.

Write a proof of the Polygon Interior Angle-Sum Theorem.The sum of the measures of the interior angles of a convex n-gon is 180 times (n-2).By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into how many triangles?

Write a proof of the Polygon Interior Angle-Sum Theorem.

The sum of the measures of the interior angles of a convex n-gon is 180 times (n-2).

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into how many triangles?