SOLUTION: Find the number of sides of a polygon if the sum of the number of sides and the number of diagonals is 66. A. 11 B. 12 C. 14 D. 16

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Question 1153291: Find the number of sides of a polygon if the sum of the number of sides and the number of diagonals is 66.
A. 11
B. 12
C. 14
D. 16
Answer by MathLover1(20849) About Me  (Show Source):
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total number of diagonals: n%28n-3%29%2F2 where+n is the number of sides
if the sum of the number of sides and the number of diagonals is 66, we have
n%2Bn%28n-3%29%2F2=66
%282n%2Bn%5E2-3n%29%2F2=66
n%5E2-n=132
n%5E2-n-132=0...factor completely
n%5E2%2B11n-12n-132=0
%28n%5E2%2B11n%29-%2812n%2B132%29=0
n%28n%2B11%29-12%28n%2B11%29=0
%28n+-+12%29+%28n+%2B+11%29+=+0
solutions:
n=12
n=-11-> disregard negative solution
the number of sides is 12
answer: B. 12