Given a regular n-gon find i, I, e and E if a) n=20 b) i=150 c) e=120 d) l=4500

Question

need help finding the answer to this problem

Answer 1

Is this high school geometry ?

assuming i=interior angle, e=exterior angle, but l=? and E=?

a) n=20

(n-2)(180)=18*180=3240º in the 20-gon

3240/20=162º in each interior angle

180-162=18º in each exterior angle

b) i=150º

180-150=30º in each exterior angle

# sides=360/ext ∠

# sides=360/30

# sides=12

(n-2)180=(12-2)180=10*180=1800º in the 12-gon

c) e=120º

180-120=60º in each interior angle

# sides=360/ext ∠

# sides=360/120

# sides=3

3-gon is a triangle

180º in a triangle

d) l=4500 ???

Is this the sum of the angles in the n-gon ? just a guess !!

If so, (n-2)180=4500

(n-2)=4500/180

n-2=25

n=27, a 27-gon

27=360/ext ∠

ext ∠=360/27=13 1/3º

interior angle=180-13 1/3=166 2/3º

Hope this helps.