The measure of an angle is eight times the measure of a complementary angle. what is the measure of each angle?

Let 'x' be the 1st angle
and the second angle is '8x'
complementary angle is equal to 90

therefore,
               x+8x=90

                9x=90

                x=90/9

                x=10 

    Hence, 1st angle= x=10

                 2nd angle=8x=80

Complementary angles have a sum of 90° (they are two angles that add up to make a right angle). 

Let's say one of these angles has a measure . The program states that its complement is eight times this, so it has measure .

We know that these angles together equal 90°, so we can write 
.

If x = 10, then the first angle has a measure of 10°, and the second angles has a measure of , or 80°.