Question

Explain how the formula for finding the sum of the interior angle measures of a polygon is derived.

Answer 1

The formula for finding the sum of the interior angle measures of a polygon is derived through a process of dividing the polygon into triangles and using the fact that the sum of angles in a triangle is always 180 degrees.

Step-by-step explanation:

The formula for finding the sum of the interior angle measures of a polygon is derived through a process of dividing the polygon into triangles. Here are the steps to derive the formula:

1. Start with any polygon with 'n' number of sides.
2. Divide the polygon into 'n-2' triangles by drawing diagonals from any one vertex.
3. Since the sum of angles in a triangle is always 180 degrees, the sum of angles in 'n-2' triangles would be (n-2) * 180 degrees.
4. The sum of angles in the polygon is equal to the sum of angles in 'n-2' triangles, so we can write the formula as (n-2) * 180 degrees.

Answer 2

Step-by-step explanation:

Here's one way:

Choose a point P interior to the polygon and draw a segment from that point to each vertex. These segments will divide an n-sided polygon into n triangles. These will have a total angle measure of ...

total interior angles of n triangles = 180°×n

The n angles having a vertex at point P have a sum of 360°. Subtracting this total from the total of all triangles gives the sum of interior angles around the perimeter of the polygon: 180°×n - 360° = 180°×(n -2).