Answer
10 sides
Work Step by Step
$D = 1/2 * n * (n-3)$
35 diagonals
$35 = 1/2 * n * (n-3)$
$35*2=1/2*2*n*(n-3)$
$70 = n(n-3)$
$n^2-3n=70$
$n^2-3n-70=0$
$n^2-10n+7n-70=0$
$n(n-10)+7(n-10)=0$
$(n-10)(n+7)=0$
$n-10=0$
$n=10$
$n+7=0$
$n=-7$ (this answer is invalid since we can't have a negative number of sides)
