Question

The exterior angle of a regular polygon
is one-third of its interior angle. Find
the number of sides of the palygon.
Select from the Answers below​

Answer 1

Answer :

• Number of sides of the polygon is 8.

Given :

• The exterior angle of a regular polygon is one - third of its exterior angle

To find :

• Number of sides of the polygon

Solution :

• Let the interior angle of a regular polygon be x

The exterior angle of a regular polygon is one - third of its interior angle so,

• 1/3 x

As we know that,

• Sum of adjacent interior and exterior angle = 180⁰

According to this,

》1/3 x + x = 180⁰

》x(1/3 + 1) = 180⁰

》x (4/3) = 180⁰

》x = 3/4 × 180⁰

》x = 3 × 45⁰

》x = 135⁰

Hence ,

• Interior angle of a regular polygon is 135⁰
• Exterior angle of a regular polygon is 135⁰/3 = 45⁰

Now , we have to find the number of sides of the polygon:

As we know that,

• Number of sides of regular polygon is 360⁰/Exterior angle

》360⁰/Exterior angle

》360/45

》8

Hence, Number of sides of the polygon is 8.