- 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

# 1. Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 5

2. PQRSTU is a regular hexagon. Determine each angle of triangle PQT.

**To find:**

1. We have to determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 5

2. We have to determine each angle of triangle PQT if PQRSTU is a regular hexagon.

**
**

**Solution:**

**1) **

Sum of interior angles of polygon =$ (2n - 4) \times 90$

Sum of interior angles = $5 \times$ sum of exterior angles = $5 \times 360$

$(2n - 4) \times 90 = 5 \times 360$

$2n - 4 = 5 \times \frac{360}{90} = 20$

or $2n = 24$ or $n = 12$

**So the required polygon has 12 sides.**

**
**

**
**

**
**

**
**

**2)**

Exterior angle of regular hexagon = $\frac{360}{6} = 60$;

Interior angle of regular hexagon =$180 - 60 = 120$

**
**

**From triangle PQT**

**
**

**The angles are 30, 30, and 120.**

**
**

Advertisements