Answer:
720°, 2340°, 180°
Step-by-step explanation:
Look at the attached image of a regular hexagon. I drew all possible lines from a vertex to other vertices (AC, AD, AE). Drawing in all those diagonals splits the hexagon into 4 triangles, and adding up the measures of all the triangle angles would account for all the interior angles of the hexagon.
♦ Four triangles have an angle sum of 180° x 4 = 720° (180° in each triangle).
See attached image2 to see what happens in an octagon. There are six triangles formed, so the total of all interior angle measures is 6 x 180° = 1080°.
What about a 15-sided regular polygon? How many triangles would be formed by putting in all the diagonals coming from one vertex? There will be 2 fewer triangles than the number of vertices, 13.
♦ The total of interior angle measures in a 15-gon is 13(180°) = 2340°
♦ A polygon with 3 sides is a single triangle; interior angle sum = 180°
