The sum of the interior angles of a polygon is a fundamental concept in geometry. It refers to the total measure of all the angles inside the polygon. Understanding this concept is crucial for working with polygons and solving geometric problems.

Simple Explanation:

What is the Sum of Interior Angles?

The sum of interior angles is the combined measure of all the angles enclosed within a polygon.

It helps us understand the relationship between the number of sides (vertices) and the total angle measure of a polygon.

Steps to Find the Sum of Interior Angles:

Count the Number of Sides:

Start by counting the number of sides or vertices (corners) of the polygon.

Use the Interior Angle Formula:

To find the sum of interior angles, use the following formula:

Sum = (n - 2) * 180 degrees

where n is the number of sides or vertices.

Example:

Sum of Interior Angles of a Triangle:

A triangle has 3 sides (n = 3).

Using the formula: Sum = (3 - 2) * 180 degrees = 1 * 180 degrees = 180 degrees.

So, the sum of interior angles of a triangle is 180 degrees.

Key Points to Remember:

The sum of interior angles formula is (n - 2) * 180 degrees, where n is the number of sides.

This concept is applicable to various polygons, not just triangles.

Activity:

Practice finding the sum of interior angles for different polygons to enhance your geometry skills.

Extra Tip:

The sum of interior angles is a fundamental property used in geometry proofs and calculations.

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