If you put an imaginary line from the base of the ladder to the wall it would from a right angled triangle. The internal angles of a triangle all add up to 180degrees. With a right angled triangle, we know for sure one angle is going to be 90 degrees. One angle as you said is 31 degrees so you just add 31 and 90 which is equal to 121 then subtract it by that. SO:
180-(31+90)
180-121=59 degrees
or even easier
90-31= 59
