Question

A polygon has d diagonals. If the polygon had one more side, it would d + 10 diagonals. How many sides does the polygon have?

Answer 1

A polygon of n sides can have n-1 diagonal from each vertex. From n vertices, the polygon can have n(n-1)/2 diagonals. The number has to be divided by 2 because we have counted the diagonal from both sides.

So using the formula
d(n)=n(n-1)/2
you can find n.

Hint: n is between 5 and 15.

Answer 2

Do me so hard MM!