Question

Help plz I can't solve it

Answer 1

1) interior angle=
`((n-2)*180)/(n)=(180n-360)/(n)=180-(360)/(n)`
exterior angle=
`(360)/(n)`

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