Unit
Polygons
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
The formula for the sum of the angles of a polygon with n sides is (n - 2)*180°. This is derived from the measure of degrees of a triangle. Recall that by the triangle angle sum theorem that the sum of the angles in a triangle is 180°. This makes sense by the formula of the sum of angles in a polygon, since (3 - 2)*180° = 1*(180°) = 180°.
For example, a dodecagon is a polygon with 12 sides. By this formula, the sum of the angles is:
Thus, the sum of the angles in a dodecagon is 1800°.
In this problem we’re being asked to apply what we know about the sum of the angles in a polygon. It says find the sum of the angles of a dodecagon. So first off what is a dodecagon? Since you have this all memorized, you remember that dodecagon means the number of sides is 12.
Our angle sum formula says that if we take the number of sides and if we subtract 2, that will give us n minus 2 triangles and the sum of a triangle, sum of the angles in a triangle is 180. So to find the angle sum, all we need to do is substitute in 12 for n, so I’m going to say 12 minus 2 times 180 degrees. 12 minus 2 is 10, so we have 10 times 180 degrees and that’s pretty easy that’s going to be 1800 degrees. So the sum of the angles, we found by using our angle formula which says n minus 2 times 180 degrees.