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Sum of Interior Angles of a Polygon: Polygonal Geometry

_{August 25, 2023 by JoyAnswer.org, Category : Mathematics}

How to find the sum of the interior angles of a polygon?Understand the formula for calculating the sum of interior angles in a polygon and how it relates to different types of polygons.

How to find the sum of the interior angles of a polygon?

Sum of Interior Angles of a Polygon: Polygonal Geometry

In polygonal geometry, the sum of the interior angles of a polygon can be calculated using the following formula:

Sum of Interior Angles = (n - 2) * 180 degrees

Where:

n is the number of sides (or vertices) of the polygon.

This formula applies to both regular and irregular polygons, as long as you know the number of sides. Here are a few examples:

1. Triangle (n = 3):

Sum of Interior Angles = (3 - 2) * 180 = 1 * 180 = 180 degrees

2. Quadrilateral (n = 4):

Sum of Interior Angles = (4 - 2) * 180 = 2 * 180 = 360 degrees

3. Pentagon (n = 5):

Sum of Interior Angles = (5 - 2) * 180 = 3 * 180 = 540 degrees

This formula can be useful for finding the total measure of the interior angles of a polygon without needing to calculate each angle individually. It applies to polygons of any size, as long as the polygon is closed and has distinct vertices.

_{Tags Interior Angle Sum , Polygon Properties , Geometric Formulas}

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