Angle Sum Property Formula
The angle sum property formula used for any polygon is given by the expression,
Sum of Interior Angle = (n − 2) × 180°
where ‘n’ is the number of sides of the polygon.
According to this property, the sum of the interior angles of the polygon depends on how many triangles are formed inside the polygon, i.e. for 1 triangle the sum of interior angles is 1×180° for two triangles inside the polygon the sum of interior angles is 2×180° similarly for a polygon of ‘n’ sides, (n – 2) triangles are formed inside it.
Example: Find the sum of the interior angles for the pentagon.
Solution:
Pentagon has 5 sides.
So, n = 5
Thus, n – 2 = 5 – 2 = 3 triangles are formed.
Sum of Interior Angle = (n − 2) × 180°
⇒ Sum of Interior Angle = (5 − 2) × 180°
⇒ Sum of Interior Angle = 3 × 180° = 540°
Angle Sum Property of a Triangle
Angle Sum Property of a Triangle is the special property of a triangle that is used to find the value of an unknown angle in the triangle. It is the most widely used property of a triangle and according to this property, “Sum of All the Angles of a Triangle is equal to 180º.”
Angle Sum Property of a Triangle is applicable to any of the triangles whether it is a right, acute, obtuse angle triangle or any other type of triangle. So, let’s learn about this fundamental property of a triangle i.e., “Angle Sum Property “.
Table of Content
- What is the Angle Sum Property?
- Angle Sum Property Formula
- Proof of Angle Sum Property
- Exterior Angle Property of a Triangle Theorem
- Angle Sum Property of Triangle Facts
- Solved Example
- FAQs