We will learn how to find the sum of the exterior angles of a polygon having n sides.
We know that, exterior angle + interior adjacent angle = 180°
So, if the polygon has n sides, then
Sum of all exterior angles + Sum of all interior angles = n × 180°
So, sum of all exterior angles = n × 180° - Sum of all interior angles
Sum of all exterior angles = n × 180° - (n -2) × 180°
= n × 180° - n × 180° + 2 × 180°
= 180°n - 180°n + 360°
= 360°
Therefore, we conclude that sum of all exterior angles of the polygon having n sides = 360°
Therefore, measure of each exterior angle of the regular
polygon = 360°/n
Also, number of sides of the polygon = 360°/each exterior angle
Solved examples on sum of the exterior angles of a polygon:
1. Find the number of sides in a regular polygon when the measure of each exterior angle is 45°.
Solution:
If the polygon has n sides,
Then, we know that; n = 360°/measure of each exterior angle
= 360/45
= 8
Therefore, the regular polygon has 8 sides.
2. The exteriors angles of a pentagon are (m + 5)°, (2m + 3)°, (3m + 2)°, (4m + 1)° and (5m + 4)° respectively. Find the measure of each angle.
Hints: The sum of all exterior angles of a polygon is 360°.
Solution:
We know, the sum of all exterior angles of a pentagon is 360°
Therefore, (m + 5)° + (2m + 3)° + (3m + 2)° + (4m + 1)° + (5m + 4)° = 360°
⇒ m + 5 + 2m + 3 + 3m + 2 + 4m + 1 + 5m + 4 = 360°
⇒ 15m + 15 = 360°
⇒ 15m = 360° - 15°
⇒ 15m = 345°
⇒ m = 345°/15°
⇒ m = 23°
Therefore, the first angle = m + 5°
= 23° + 5°
= 28°
Second angle = 2m + 3°
= 2° × 23° + 3°
= 46° + 3°
= 49°
Third angle = 3m + 2
= 3° × 23° + 2°
= 69° + 2°
= 71°
Fourth angle = 4m + 1
= 4° × 23° + 1°
= 92° +1°
= 93°
Fifth angle = 5m + 4°
= 5° × 23° + 4°
= 115° + 4°
= 119°
● Polygons
Polygon and its Classification
Interior and Exterior of the Polygon
Number of Triangles Contained in a Polygon
Angle Sum Property of a Polygon
Problems on Angle Sum Property of a Polygon
Sum of the Interior Angles of a Polygon
Sum of the Exterior Angles of a Polygon
7th Grade Math Problems
8th Grade Math Practice
From Sum of the Exterior Angles of a Polygon to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 17, 24 01:53 PM
Apr 17, 24 01:32 PM
Apr 16, 24 02:00 AM
Apr 16, 24 01:15 AM
Apr 15, 24 11:30 PM
● Polygons - Worksheets
Worksheet on Polygon and its Classification
Worksheet on Interior Angles of a Polygon
Worksheet on Exterior Angles of a Polygon