You first find the other angles of the triangle. One is 90 degrees at the corner. The other would be 40 because the outside angle is 140 and that is 40 away from 80. Add 40 and 90 together to get 130 degrees. Subtract that from 180 and that is 50 degrees :)
The ladder is forming a right triangle with the house. In this right triangle the hypotenuse is the measure of the ladder, and the distance between the house and he ladder is one of the sides of the triangle. To find the angle, , that the ladder is making with the ground, we are going to use a trig function that relates the adjacent side of our angle with the hypotenuse. That trig function is Cosine.
We can conclude that the ladder make with the ground a 62° angle.