The total number of sides in two regular polygons is 13, and total number of diagonals is 25. how many sides are in each polygon?

Let x be the sides of one polygon
y be the sides of the other polygon

x + y = 13
y = 13 - x

then the formula for the number of polygons is n(n - 3) / 2

x(x - 3) / 2  + y(y - 3) / 2 = 25
x(x - 3) / 2 + ( 13 - x) ( 13 - x - 3) / 2 = 25
x( x - 3 ) / 2 + ( 13 - x) ( 10 - x) / 2 = 25

solve for x
x = 8
y = 13 - 8 = 5