What is the sum of the angle measurement of a decagon?

Pick a point around the center of the polygon. Join each vertex to this point. You will now have 10 triangles. The total angle of these 10 triangles is 10x180 degrees. Now you need to subtract the angles of the ten triangles at the center (which is 360 degrees). Therefore total internal angles is (10x180)-360 = 1800-360 which is 1440 degrees.