How do you calculate the degrees of a polygon?

To calculate the sum of the interior angles of a polygon, you can use the formula that relates to the number of sides, denoted as ( n ). The correct formula is ( 180(n-2) ). This formula emerges from the fact that any polygon can be divided into triangles. Since the sum of the angles in a triangle is 180 degrees, and a polygon with ( n ) sides can be divided into ( (n-2) ) triangles, we multiply the number of triangles by 180 degrees, yielding the total sum of the interior angles.

For instance, a triangle (3 sides) has a total angle measure of ( 180(3-2) = 180 ) degrees, while a quadrilateral (4 sides) has ( 180(4-2) = 360 ) degrees, and so forth. This pattern holds true for any polygon.

The other formulas provided do not correctly represent the sum of interior angles. One suggests using 90 degrees, which does not apply to the calculation of polygon angles. Another using 360 degrees incorrectly assumes a relationship that does not exist for calculating interior angles, and the formula using ( 180n ) inaccurately represents the angle sum by