Interior Angles Theorem
Statement: For a polygon of ‘n’ sides, sum of the interior angles is always equal to (n – 2) × 180°.
To prove: Sum of Interior Angles in any Polygon = (2n – 4) right angles
Proof:
Consider a polygon with n sides in which n triangles are formed. ABCDE is a “n” sided polygon shown in the image added below:
Take any point O inside the polygon. Join OA, OB, OC, OD and so on.
We know that,
Sum of interior angles of triangle = 180°
Polygons with n sides have n triangles
So, total sum interior angles of n triangles = n × 180°
Sum of interior angles of polygon + Angles at center O = n × 180°…(i)
Sum of angles at center O = 360°
Putting in equation (i)
Sum of interior angles of the polygon = (n × 180°) – 360°
Sum of Interior Angles of Polygon = (n – 2) × 180° = (2n – 4) × 90° = (2n – 4) Right Angles
Hence Proved.
Interior Angles of a Polygon
Interior angles of a polygon are angles within a polygon made by two sides. The interior angles in a regular polygon are always equal. The sum of the interior angles of a polygon can be calculated by subtracting 2 from the number of sides of the polygon and multiplying by 180°. Sum of Interior Angles = (n − 2) × 180°
In this article, we will learn about the interior angles of a polygon, the sum of interior angles of a polygon, the formula for the interior angles, and others in detail.
Table of Content
- What is Angle?
- What are Interior Angles of Polygons?
- Sum of Interior Angles Formula
- Interior Angles Theorem
- Sum of Interior Angles of a Polygon
- Interior Angles in Different Types of Polygons
- Interior and Exterior Angles of a Polygon
- Exterior Angles
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