More Lessons for Grade 9

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Videos, worksheets, solutions, and activities to help Geometry students learn about interior angles of polygons.

Sum of interior angles in a polygon = (n - 2)180°, where n is the number of sides in the polygon.

This is also called the polygon angle sum theorem.

An equilateral polygon is a polygon with all sides equal.

An equilateral polygon is a polygon with all angles equal.

An regular polygon is a polygon which is both equilateral and equiangular.

Each interior angle of a regular polygon = \(\frac{{\left( {n - 2} \right)180^\circ }}{n}\), where n is the number of sides in the polygon.

Polygon Angle Sum Theorem

The sum of the angles in any polygon is equal to the number of sides in the polygon minus two, all multiplied by 180 degrees. Sum of polygon angles problems may ask you to determine the sum of angles in a particular type of polygon, the number of sides when given the sum of polygon angles, or a particular angle given the other angles in the polygon.

Students learn the definitions of vertices and diagonals of polygons. Students also learn the following formulas related to convex polygons. The sum of the measures of the interior angles of a polygon is always 180(n - 2) degrees, where n represents the number of sides of the polygon.

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