Question

Fill in the blanks to complete the inference chart.
Write your answers in order.

Answer 1

1. triangles
2. 180°
3. triangles, 180°

Explanation:

A diagonal divides a polygon into two parts. Drawing all of the diagonals from a given vertex to the other non-adjacent vertices will divide the polygon into triangles.

The angle sum theorem tells you the sum of triangle angles at any polygon vertex will be equal to the measure of the interior angle of the polygon at that vertex. Since we're concerned only with triangles created by drawing diagonals between non-adjacent polygon vertices, the sum of triangle angles will be the sum of polygon angles.

So, you can multiply the number of triangles by 180° to find the sum of interior angles of the polygon. (The number of triangles is two fewer than the number of polygon sides.)