# INTERIOR ANGLES OF A POLYGON

## About "Interior angles of a polygon"

Interior angles of a polygon :

Here we are going to learn how to find interior angles of polygon.

We can calculate interior angle of polygon by using the formula given below.

Measure of each angle

=  [(n -2) x 180°]/number of sides

Example 1 :

Find the measure of one interior angle in each polygon.

Solution :

According to the formula, first let us count the number of sides of the polygon.

AB, BC, CD, DE, EA total number of sides are 5.

Sum of interior angles of polygon  =  (n - 2) x 180°

=  (5 - 2) x 180°

=  3 x 180°

=  540°

Measure of each angle  =  540°/5  =  108°

Hence the measure of each interior angle of the pentagon is 108°.

Example 2 :

Find the measure of one interior angle in each polygon.

Solution :

According to the formula, first let us count the number of sides of the polygon.

AB, BC, CD, DE, EF, FG, GH, HA total number of sides are 8.

Sum of interior angles of a polygon  =  (n - 2) x 180°

=  (8 - 2) x 180°

=  6 x 180°

=  1080°

Measure of each angle  =  1080°/8  =  135°

Hence the measure of each interior angle of the given  polygon is 135°.

Example 3 :

Find the measure of one interior angle in each polygon.

Solution :

According to the formula, first let us count the number of sides of the polygon.

AB, BC, CD, DE, EF, FG, GH, HI, IJ, JK, KA total number of sides are 11 .

Sum of interior angles of a polygon  =  (n - 2) x 180°

=  (11 - 2) x 180°

=  9 x 180°

=  1620°

Measure of each angle  =  1620°/11  =  147° 3'

Hence the measure of each interior angle of the given 11 sided polygon is 147° 3'.

Example 4 :

Find the measure of one interior angle in each polygon.

Solution :

According to the formula, first let us count the number of sides of the polygon.

AB, BC, CD, DE, EF, FA total number of sides are 6.

Sum of interior angles of a polygon  =  (n - 2) x 180°

=  (6 - 2) x 180°

=  4 x 180°

=  720°

Measure of each angle  =  720°/6  =  120°

Hence the measure of each interior angle of the given 6 sided polygon is 120°.

After having gone through the stuff given above, we hope that the students would have understood "Interior angles of polygon".

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