What is the relationship between the number of triangles created by the diagonals of apolygon and the sum of the interior angle measures of a polygon?

To understand the relationship between the number of triangles created by the diagonals of a polygon and the sum of the interior angle measures of a polygon, we can follow these steps:

Step 1: Determine the number of triangles created by the diagonals of a polygon.

• For any polygon with n sides, we can draw diagonals from one vertex to all other non-adjacent vertices.
• The number of triangles formed by these diagonals can be calculated using the formula: (n-2)(n-3)/2.

Step 2: Calculate the sum of the interior angle measures of a polygon.

• The sum of the interior angle measures of a polygon can be found using the formula: (n-2) * 180 degrees.
• Here, n represents the number of sides of the polygon.

Step 3: Compare the number of triangles with the sum of the interior angle measures.

• By comparing the number of triangles created by the diagonals with the sum of the interior angle measures, we can observe a relationship.
• Generally, the number of triangles formed by the diagonals is equal to the sum of the interior angle measures divided by 180 degrees.

In conclusion, the relationship between the number of triangles created by the diagonals of a polygon and the sum of the interior angle measures of a polygon is that the number of triangles is equal to the sum of the interior angle measures divided by 180 degrees.