PROBLEMS ON REGULAR POLYGON

Problem 1 :

Find the number of sides of a regular polygon which has angles of 150°

Solution :

Sum of the angles of a regular polygon = 150

Let n be the number of sides.

n = 12

So, the number of sides of a required polygon is 12.

Problem 2 :

Is there a regular polygon which has the angle of 158°

Solution :

Here we get the value of n as decimal. So, there is no such regular polygon is having an angle of 158°.

Problem 3 :

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 = 6, number of angles = 6

e) Octagon

Number of sides = 8, number of angles = 8

f) Decagon

Number of sides = 10, number of angles = 10