Solve the problem.
-If a polygon, of n sides has $$\frac { 1 } { 2 } n ( n - 3 )$$ ) diagonals, how many sides will a polygon with 189 diagonals have?
A) 22 sides
B) 21 sides
C) 20 sides
D) 23 sides

Question

Quizplus · Accepted Answer

Given the formula for the number of diagonals in a polygon is $\frac{1}{2}n(n-3)$, where $n$ is the number of sides. To find the number of sides for a polygon with 189 diagonals, we set the formula equal to 189 and solve for $n$: $\frac{1}{2}n(n-3) = 189$. Simplifying, we get $n^2 - 3n - 378 = 0$. Solving this quadratic equation, we find that $n = 21$ is the positive solution that makes sense in the context of a polygon.

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