How do you calculate the angle sum of a polygon?

Answer 1

In any polygon the sides can all be joined to the middle by lines coming from the corners. Each pair of these lines, and the side of the ploygon which joins them makes a triangle.

In an X-sided polygon there will be X triangles

The angles of a triangle always add up to 180º.

Multiply the number of sides by 180 and you'll get a certain figure = 180X.

The centre of the polygon where the triangles all meet is a circle, so we need to subtract that from the 180X. A circle is 360º.

So the formula which works out the angle sum of a polygon is (180X - 360)º.

If the polygon is regular, then the individual angles will be ((180X - 360) / X)º.