# Find the number of vertices of a polygon having 495 diagonals

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**Answer:**

**Step-by-step explanation:**

Answer:33 sides

Step-by-step explanation:

The number of diagonals of a polygon is equal to:

d=n(n-3)/2 where n is the number of sides.

So you would say:

495=n(n-3)/2

990=n(n-3)

0=n^2-3n-990

0=(n-33)(n+30)

n=33 or -30

But it cannot equal -30 because a polygon cannot have a negative quantity of sides. So the answer is 33 sides

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