How do you calculate the total degrees in a polygon?

To determine the total degrees in a polygon, you can use the formula that involves the number of sides of the polygon. Specifically, the total interior angle measure of a polygon can be calculated by taking the number of sides, subtracting two, and then multiplying by 180 degrees. This formula arises from the fact that any polygon can be divided into triangles.

For instance, a triangle (which has 3 sides) can be seen as having 1 triangle formed when you connect two of its vertices to a non-adjacent vertex. Since each triangle has a total of 180 degrees, the formula accounts for the additional sides beyond a triangle. For any polygon with 'n' sides, the number of triangles formed is 'n-2', which is why we use (n - 2) x 180 to find the total degrees of the polygon.

This understanding helps apply the formula accurately for any polygon: a quadrilateral (4 sides) has (4 - 2) x 180 = 360 degrees, a pentagon (5 sides) has (5 - 2) x 180 = 540 degrees, and so forth. This consistent method provides an effective means to determine the total degrees for more complex polygons as well