SOLUTION: A polygon has m sides. If one of its interior angles is 80 degrees, and the other interior angles are each equal to 160 degrees, find the value of m.

Question 725369: A polygon has m sides. If one of its interior angles is 80 degrees, and the other interior angles are each equal to 160 degrees, find the value of m.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If there are m sides, then the angles sum up to 180(m-2) degrees
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There is 1 angle that is 80 degrees

There are m angles total, so this means that there are m-1 angles left (if one is already taken). These m-1 angles are all 160 degrees.

So

80 + 160(m-1) = 180(m-2)

Solve for m:

80+160(m-1)=180(m-2)

80+160m-160=180m-360

160m-80=180m-360

160m=180m-360+80

160m-180m=-360+80

-20m=-360+80

-20m=-280

m=(-280)/(-20)

m=14

So there are 14 sides (and 14 angles).

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