Question

Explain how the formula for finding the sum of the interior angle measures of a polygon is derived. (Site 1)

Answer 1

The formula for finding the sum of the interior angles of a polygon is the same, whether the polygon is regular or irregular. So you would use the formula (n-2) x 180, where n is the number of sides in thepolygon. If you draw a diagonal in the square, that forms two triangles.

Answer 2

Construct a polygon, with n sides.

For a triangle to occur, you cannot join the adjacent points from a fixed point. Thus, the maximum amount of triangles you can make in an n-sided shape is (n - 2).
Since we're slicing down the polygon into triangles, we can find that the three angles have to add up to 180°.

Thus, the general formula becomes:
180(n - 2), where n is the number of sides of the polygon.

Let's verify this with a square/rectangle.
They have 4 sides, so the summation of the interior angles become: 180(4 - 2) = 360, which is indeed correct.