# What is the sum of the angles of a decagon?

September 24, 2021 | education

| We are given a convex polygon (decagon) with n = 10 corners.

If you draw diagonals from each corner to opposite corners, then the diagonals will split it into (n-2) triangles.

The sum of the angles of the polygon coincides with the sum of the angles of the resulting triangles. The sum of the angles in a triangle is 180 degrees, so the sum of this polygon is (n-2) * 180 – the theorem on the sum of angles in a polygon.

Let’s apply for our polygon:

(10-2) * 180 = 1440 degrees.

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