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Find Interior Angles of Polygons




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

How to calculate the sum of interior angles in any polygon?
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.

What is an equilateral polygon?
An equilateral polygon is a polygon with all sides equal.

What is an equiangular polygon?
An equilateral polygon is a polygon with all angles equal.

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

How to calculate the interior angle of a regular polygon?
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.
Sum of Interior Angles of a 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.



Using the sum of a polygon's interior angles to solve for a missing angle
Given an irregular hexagon; finding the sum of the interior angles using the sum of the interior angles formula, and then setting up an equation equal to this sum to find the value of x in each of the angle expressions. Upon finding the value of x, substituting that value in for the variable in each of the expressions to find the angle measure of each of the six angles.


 

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