Sum of the Measures of the Exterior Angles of a Polygon


 
 
Concept Explanation
 

Sum of the Measures of the Exterior Angles of a Polygon

In a polygon is the sides are produced in order we will get the exterior angles as shown below. The exterior angles are marked as A, B, C, D, E, F

Sum of exterior angles of a polygon for any number of sides = 3600

angle A+angle B+angle C+angle D+angle E = 360^0

Regular Polygon:

A regular polygon is a polygon which has sides of equal length and all interior angles are also equal. All the exterior angles are also equal. So if there is a regular polygon of n sides where n>= 3 then its each exterior  angle

 =frac{360^0}{n}

Illustration: Find the sum of exterior angles of a 15 sided polygon.

Solution:The sum of exterior angle of a polygon is independent of the number of sides

Hence the sum of exterior angles of a 15 sided polygon is 3600.

Illustration: How many sides does a regular polygon has if its each exterior angle is a measure of 240?

Solution:Let us suppose the polygon has n sides

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Sample Questions
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Question : 1

The exteriors angles of a pentagon are (m + 5)°, (2 m + 3)°, (3 m + 2)°, (4 m + 1)° and (5 m + 4)° respectively. Find the measure of each angle.

Right Option : B
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Explanation
Question : 2

Find the number of sides of a regular polygon if each exterior angle measures:  120^{0}

 

Right Option : B
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Explanation
Question : 3

How many sides a regular polygon  has whose each exterior angle is 45?

Right Option : A
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Explanation
 
 
 
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