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, we can set this equal to 189 to solve for $n$: $\frac{1}{2}n(n-3) = 189$. Solving this quadratic equation for $n$ gives $n = 21$.

Solve the Problem nnn Sides Has 12n(n−3)\frac { 1 } { 2 } n ( n - 3 )21​n(n−3)

Solve the Problem $n$ Sides Has $\frac { 1 } { 2 } n ( n - 3 )$