1) Let's use B and D to solve x first:
B + D = 180, because their opposite arcs total 360 (whole circle), and inscribed angles are 1/2 of their opposite arcs
x+10 + x+24 = 180
2x + 34 = 180
2x +34-34 = 180-34
2x = 146
x = 73
2) now that we have x, let's use the same time to show that A + C = 180
x+15 + C = 180
73+15 + C = 180
C +88-88 = 180-88
C = 92°