In a regular polygon there are two diagonals such that the angle between them is 50 degrees. What is the smallest number of sides of the polygon for which this is possible?

I had thought that for this to be the case, the smallest possible angle between diagonals of a polygon must be a factor of 50.

Factors of 50: 1, 50, 2, 25, 5, 10

Let x be the number of sides of the polygon

The biggest factor that lets x be a whole number is 10.

WRONG!

Answer is 18.