An angles measure is eight times the measure of its complement the larger angle is how many more degrees larger than the smaller angle?

Two angles are complementary when they add up to 90 degrees 

smaller angle = x
larger angle = 8x

x + 8x = 90
9x = 90
x = 90/9
x = 10°  ← smaller angle

larger angle = 8x = 8 * 10 = 80°

80° - 10° = 70°

The larger angle is 70° larger than the smaller angle