Question 78

Find the internal angle of a polygon with 35 diagonals. 

Solution

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Number of diagonals can be found by using: $$^nC_2-n$$
$$\frac{n\left(n-1\right)}{2}-n=35$$
$$n^2-3n-70=0$$
$$\left(n-10\right)\left(n+7\right)$$

N cannot be negative so n=10

Internal angle can be calculated using, 
$$\frac{180\left(n-2\right)}{n}=\frac{180\left(8\right)}{10}=144$$

Hence the answer is 144. 

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