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

2 Answers
Jul 29, 2018

Answer:

The sum of the exterior angles is always #360°#

Explanation:

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 xx 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 xx72° = 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 xx 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#

#=(180n-(180(n-2)))/n#

#=(180n-180n+360)/n#

exterior angle #=360/n#

The sum #= 360/n xx n = 360°#

Jul 29, 2018

Answer:

#360^@#

Explanation:

#"The sum of the exterior angles of any polygon is "360^@#