What is the sum of the exterior angles of a polygon with 4 sides? 5 sides? 6 sides? n sides?

Nicholas Hunter 2022-11-21 Answered
What is the sum of the exterior angles of a polygon with 4 sides? 5 sides? 6 sides? n sides?
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Answers (2)

lelestalis80d
Answered 2022-11-22 Author has 23 answers
Step 1
The interior angle of a polygon can be found by:
180 ( n - 2 ) n where n is the number of sides
a) 4 sides
Interior angle is equal to:
180 ( 4 - 2 ) 4 = 90
Therefore, exterior angle is equal to 180 - 90 = 90
The sum = 4 × 90 ° = 360 °
b) 5 sides
Interior angle is equal to:
180 ( 5 - 2 ) 5 = 108
Therefore, exterior angle is equal to 180 - 108 = 72
The sum = 5 × 72 ° = 360 °
c) 6 sides
Interior angle is equal to:
180 ( 6 - 2 ) 6 = 120
Therefore, exterior angle is equal to 180 - 120 = 60
The sum = 6 × 60 ° = 360 °
d) n sides
Interior angle is equal to:
180 ( n - 2 ) n
So exterior angle is equal to 180 - 180 ( n - 2 ) n which can be simplified
180 - 180 ( n - 2 ) n
= 180 n - ( 180 ( n - 2 ) ) n
= 180 n - 180 n + 360 n
exterior angle = 360 n
The sum = 360 n × n = 360 °
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Aleah Avery
Answered 2022-11-23 Author has 4 answers
The sum of the exterior angles of any polygon is 360
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