# Interior Angles of a Polygon

Polygons

## Definition

An interior angle of a polygon is an angle formed inside the polygon by two adjacent sides.

## Description

In geometry, interior angles play a crucial role in understanding the properties and classifications of polygons. A polygon is a closed shape with straight sides, and the interior angles are the angles formed at each vertex inside the polygon. The sum of the interior angles of a polygon depends on the number of sides the polygon has. This sum can be calculated using the formula: Sum of Interior Angles = 180 ( š ā 2 ) Sum of Interior Angles=180(nā2) where š n is the number of sides. For example, a triangle (3 sides) has a sum of interior angles equal to 180 degrees, while a quadrilateral (4 sides) has a sum of 360 degrees.

Interior angles are essential for determining the shape and symmetry of polygons. In regular polygons, where all sides and angles are equal, each interior angle can be found by dividing the sum of the interior angles by the number of sides. For instance, in a regular pentagon (5 sides), each interior angle is 108 degrees. Understanding these angles helps in various applications, including tiling patterns, architectural designs, and computer graphics.

For a complete collection of terms related to polygons click on this link: Polygons Collection.

Common Core Standards CCSS.MATH.CONTENT.5.G.B.3, CCSS.MATH.CONTENT.5.G.B.4, CCSS.MATH.CONTENT.3.G.A.1, CCSS.MATH.CONTENT.3.MD.D.8, CCSS.MATH.CONTENT.6.G.A.1, CCSS.MATH.CONTENT.6.G.A.3, CCSS.MATH.CONTENT.HSG.CO.A.3 3 - 8 Geometry     • Polygons         • Definition of a Polygon 2021 polygon, definitions, glossary term