I am having trouble with these two problems.
Both are pretty straight forward. You need to know that the degree measure of an arc is (by definition) the same as the angle it makes with the center of the circle and twice the angle it makes with a point on the circle (as in KPH of problem 7).
(7) Since the angle H is 26 degrees, arc KP has measure 2(26)= 52 degrees. Since P is the midpoint, arc PF is also 52 degrees. Drawing the radius OF gives a right triangle in which angle POF has measure 52 degrees. x, then, is 90- 52= 38 degrees.
(8) Drawing the radius from O to L gives a right triangle. The angle ROL has measure 90- 29= 61 so the arc, x, is 61 degrees.