Sum of Angles of a Polygon - JSS2 Mathematics Lesson Note

Sum of Interior Angles

The sum of the interior angles of a polygon depends on the number of sides (n) the polygon has. The formula to find the sum of the interior angles of an n-sided polygon is:

Sum of interior angles =(𝑛−2)×180∘

Example

Triangle (3 sides):

Sum of interior angles =(3−2)×180∘

=1×180∘

=180∘

Sum of interior angles=(3−2)×180 ∘

 =1×180 ∘

 =180 ∘

Each interior angle in an equilateral triangle is 180∘/3

=60∘ 

Quadrilateral (4 sides):

Sum of interior angles

=(4−2)×180∘

=2×180∘=360∘

Sum of interior angles=(4−2)×180 ∘

 =2×180 ∘

 =360 ∘

If it’s a square, each interior angle is 360∘/4

=90∘

Pentagon (5 sides):

Sum of interior angles

=(5−2)×180∘

=3×180∘=540∘

Sum of Exterior Angles

For any polygon, the sum of the exterior angles is always 360∘, no matter how many sides the polygon has.

Example

Hexagon (6 sides):

Each exterior angle in a regular hexagon is 360∘/6

=60∘