FIND THE MEASURE OF EACH INTERIOR ANGLE OF A REGULAR POLYGON

Problem 1 :

For the following regular polygon given below,

find

(i)  Number of sides that the polygon has

(ii) Number of angles

(iii)  Size of each angle.

Solution :

a) Equilateral triangle

Number of sides = 3, number of angles = 3

b) Square

Number of sides = 4, number of angles = 4

c) Pentagon

Number of sides = 5, number of angles = 5

d) Hexagon

Number of sides = 5, number of angles = 5

e) Octagon

Number of sides = 8, number of angles = 8

f) Decagon

Number of sides = 10, number of angles = 10

Problem 2 :

Find the size of each angle of a regular 12 sided polygon.

Solution :

Sum of interior angles of 12 sided polygon = (12 - 2) x 180

= 10 x 180

= 1800

Each angle measure = 1800/12

= 150

So, the size of each angle of a 12 sided regular polygon is 150 degree.

Problem 3 :

Each exterior angle of a regular polygon is 20⁰. Work out the number of sides of the polygon.

Solution :

Exterior angle of a regular polygon = 20

Interior angle = 180 - 20

Each interior angle = 160

So, the polygon will have 18 sides.