In a regular polygom of n sides each interior angle is 5 times the exterior angle. Find N
Answers
Step-by-step explanation:
3
If each interior angle of a polygon is five times the exterior angle, how many sides has the polygon?
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John Randall
Answered April 10, 2020
An n -sided regular polygon can be constructed with n isosceles triangles, each of whose apex angle is
2πn
radians. Each of the two remaining angles is
12(π−2πn)
radians, so that each interior angle is
π−2πn
radians. Each exterior angle, ϕ is
ϕ=π−(π−2πn)=2πn
radians. It’s a given in the problem statement that each interior angle is 5 times each exterior angle, so
π−2πn=10πn⟹n=12 sides
hope it may help you.
Answer:
g the planet the planet