complimentary angles are 2 angles, when added, add up to 90 degrees. So when one angle = x, its complimentary angle = (90 - x)
the measure of an angle, lets call it x, is 8 times as great (means u multiply it by 8) as the measure of its compliment...
x = 8(90 - x)
x = 720 - 8x
x + 8x = 720
9x = 720
x = 720/9
x = 80 <=== the measure of the angle is 80 degrees
its compliment is 90 - x = 90 - 80 = 10