Sum of Angles Formula
We use the sum of angles formula to determine the sum of interior angles of a polygon. The sum of angles in a polygon depends on the number of vertices it has. When there is a polygon with four or more than four sides, we draw all the possible diagonals from one vertex. Then the polygon is broken into several nonoverlapping triangles. Let us learn about the sum of angles formula with a few examples in the end.
What Is the Sum of Angles Formula?
The formula for interior angles can be determined by multiplying the number of triangles by 180°and the total number of triangles is two less than the number of sides of a polygon, always. The sum of angles formula of a given polygon can be expressed as,

The sum of its interior angle of a given polygon = ( n − 2) × 180°

The sum of exterior angles of a given polygon = 360°
Let us see the applications of the sum of angles formula in the following section.
Solved Examples Using Sum of Angles Formula

Example 1: George cuts a piece of paper into a regular pentagonal polygon and he wants to know the sum of interior angles of the regular pentagon.Find the sum of interior angles of a regular pentagon for George.
Solution:
To find: The sum of interior angles of a regular pentagon.
Sides of pentagon (n) = 5 (given)
Using sum of angles formula,
The sum of its interior angle of a given polygon (S) = ( n − 2) × 180°
S = ( 5 − 2) × 180°
= (3) × 180°
= 540°
Answer: The sum of the interior angles of a regular pentagon is 540°

Example 2: Harry wants to find the interior angle of the hexagon brick. Help him to find the measure of each interior angle of a regular hexagon?
Solution:
To find: The measure of each interior angle of a regular hexagon
Sides of Hexagon (n) = 6 (given)
Using sum of angles formula,
The sum of its interior angle of a given polygon (S) = ( n − 2) × 180°
S=( 6 − 2) × 180°
= (4) × 180°
S = 720°
The measure of each interior angle of a regular hexagon = 720°/6 = 120°
Answer: The measure of each interior angle of a regular hexagon brick is 120°