Pentagon is a two dimensional figure which has five sides and five inside angles. In pentagon, All sides are equal lengths. It is also called as five sided polygon with five angles. Pentagon is a type of plane geometry.
Exterior angle is an angle formed by any side of pentagon shape and the extension of adjacent side. In pentagon, we can made up of three triangles inside. The sum of exterior angle and interior angle is 180 degrees. Sum of exterior angles of pentagon is 360 degrees. Pentagon has five equal exterior angles.
Pantagon Angles
Steps to Calculate Exterior Angle of Pentagon:
Before we are going to calculate exterior angle of pentagon, we need to know interior angle of pentagon. Because using interior angle of pentagon, we can calculate exterior angle of pentagon. Pentagon has five equal interior angles.
Let us see how to find interior angle of pentagon.
Formula:
Sum of interior angle of Pentagon = ( n - 2) x 180
Here n is number of sides.
Pentagon has five number of sides.
So, sum of interior angle of pentagon = ( 5 - 2 ) x 180
= 3 x 180
= 540
Sum of interior angles of pentagon is 540 degrees.
Each interior angle of pentagon = sum of interior angle of pentagon / number of sides
= 540 / 5
= 108 .
An interior angle of pentagon is 108 degrees.
Interior angle of pentagon = 108
Exterior angle of pentagon = 180 - interior angle of one side
= 180 - 108
= 72
So, exterior angle of pentagon is 72 degrees.
Sum of exterior angles of pentagon = exterior angle x number of sides
= 72 x 5
= 360
So, Sum of exterior angles of pentagon is 360 degrees.
Example Problem Using Interior Angle of Pentagon:
Find the number of sides of pentagon if the sum of interior angles of pentagon is 540 degrees.
Solution:
Sum of interior angles of pentagon = ( n - 2) x 180