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# number of sides, given diagnols

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In a closed polygon, there are 35 diagonals. How many sides does the polygon have?

Answer: 10

Jun 3, 2018

### 2+0 Answers

#1
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Hello, again Ant101!

The formula to find the number of diagonals in a closed polygon is: $$\frac{n(n-3)}{2}$$ , where n is the number of sides.

Since there are 35 diagonals in the polygon, we can let the above formula equal 35.

So, we have: $$\frac{n(n-3)}{2}=35$$

Taking 2 to the other side, we have: $$n(n-3)=70$$

We need to find a value of n that suits this scenario, therefore $$\boxed{10}$$ sides is our answer!

Check: 10*(10-3)=70, 10*7=70, yep!  Jun 3, 2018
#2
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The formula to find the number of diagonals = n(n-3)/2, where n = no. of sides of the polygon.

Here n(n-3)/2 = 35, or

n(n-3) = 70

n^2 - 3n - 70 = 0, or

(n-10)(n+7) = 0, lor

n = 10 or -7.

Jun 3, 2018