- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Find the number of sides of a regular polygon if the exterior angle is one-third of its interior angle.

**Given :**

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

**To do :**

We have to find the number sides of the polygon.

**Solution :**

Let the number of sides of the regular polygon be 'n'.

The exterior angle of a regular polygon with n sides $= \frac{360}{n}$

The interior angle of a regular polygon with n sides $=180 - \frac{360}{n}$

Here, the exterior angle is one-third of its interior angle.

$\frac{360}{n} = \frac{1}{3}(180 - \frac{360}{n})$

$\frac{360\times 3}{n} = 180 - \frac{360}{n}$

$\frac{360\times 3}{n} = \frac{180 n - 360}{n}$

$360\times 3 =180 n - 360 $ [n on both sides get cancelled]

$360\times 3 + 360=180 n $

Take 360 as common in LHS,

$360(3 + 1) = 180 n $

$360 \times 4 = 180 n$

Rewrite,

$180 n = 360 \times 4$

$n = \frac{360 \times 4}{180}$

$n = 2 \times 4$ $[\frac{360}{180} = 2]$

$n = 8$

**Therefore, the number of sides of the regular polygon is 8.**

- Related Articles
- Each interior angle of a regular polygon is four times the exterior angle. Find the number of sides in the polygon.
- Find the number of sides of a regular polygon whose each exterior angle is half of it\'s interior angle
- The interior angle of a regular polygon is $156$ . Find the number of sides of the polygon.
- In a regular polygon each interior is thrice the exterior angle then number sides have?
- Program to find the Interior and Exterior Angle of a Regular Polygon in C++
- What will be the exterior angle of a polygon if the interior angle is 80 degrees?
- If an angle is one-third of its complement, find the angle.
- (a) What is the minimum interior angle possible for a regular polygon? Why?(b) What is the maximum exterior angle possible for a regular polygon?
- What is the ratio of interior and exterior angle of a regular octagon
- 1. Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 52. PQRSTU is a regular hexagon. Determine each angle of triangle PQT.
- What's the minimum exterior angle possible of a regular polygon?
- Solve the following:The sum of interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.
- How many sides does a regular polygon have if each of its interior angles is 108°?
- How many sides does a regular polygon have, if each of its interior angles is 165?
- If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.