1) interior angle= [tex] \frac{(n-2)*180}{n}=\frac{180n-360}{n}=180-\frac{360}{n}[/tex]
exterior angle=[tex]\frac{360}{n} [/tex]
notice: interior angle=180-exterior angle
->
exterior angle=180-interior angle
a)
180-150=30
b)
180-175=5
c)
180-162=18
d)
180-174=6
2)
a) octagon: n=8
exterior: 360/8=45
interior: 180-(360/8)=180-45=135
b) decagon: n=10
exterior: 360/10=36
interior: 180-(360/10)=180-36=144
3)
a) interior: 180-(360/12)=180-30=150
b) total =interior*n=144*12=1440
4)
a) interior: 180-(360/20)=180-18=162
b) total =interior*n=162*18=3240
5) pentagon: n=5
exterior: 360/5=72
6)
360/n=12
360=12n
30=n
7)
a)
i)180-(360/n)=150
180-150=360/n
30n=360
n=12
ii)180-(360/n)=175
180-175=360/n
5n=360
n=72
iii)180-(360/n)=162
180-162=360/n
18n=360
n=20
iv)180-(360/n)=174
180-174=360/n
6n=360
n=60
b) interior=123=180-exterior
exterior=180-123=57
in regular polygons the sum of all exterior angles is 360
360/exterior=amount of sides
360/57=6,3...
=not an integer -> can't be a polygon
