SOLUTION: Determine if it is possible for a regular polygon to have an interior angle with the given angle measures. Explain you reasoning. a.165 b.171 c.75

Algebra ->  Polygons -> SOLUTION: Determine if it is possible for a regular polygon to have an interior angle with the given angle measures. Explain you reasoning. a.165 b.171 c.75       Log On


   

Question 954797: Determine if it is possible for a regular polygon to have an interior angle with the given angle measures. Explain you reasoning.
a.165 b.171 c.75 d.40
Please show the work.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Interior angles for a polygon follow the formula,
A=180%28n-2%29%2Fn
a)180%28n-2%29=165n
180n-360=165n
15n=360
n=24
.
.
b) 180%28n-2%29=171n
180n-360=171n
9n=360
n=40
.
.
c) 180%28n-2%29=75n
180n-360=75n
105n=360
n=24%2F7 <--- Not an integer
You could have also guessed that since a triangle (3 sides) has an interior angle of 60 and a square (4 sides) has an interior of 90, a value between 60 and 90 would not work.
.
.
d) 180n-360=40n
180n-360=40n
140n=360
n=18%2F7 <--- Not an integer
You could have also guessed since a triangle has the fewest sides and it's interior angle is 60. So any angle less than 60 would not work.
.
Only a and b are valid interior angles.