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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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