The measure of an angle is twenty-four times the measure of its complementary angle. What is the measure of each angle?

Answer 1

By definition, the sum of the measures of complementary angles is 90 degrees.

(Note: for purposes of simplicity, I have left off the degree mark in most instances, other than the final answer.)

x + y = 90 = x + (24x) = 25x

25x =90

x = 90 / 25 = 3.6

The smaller angle measures 3.6 degrees, and the larger angle measures 24 × 3.6 = 86.4 degrees.

It is easy to check these answers by adding them together; their sum, as expected, is 90 degrees.

Answer 2

Let's the value of an angle is x' then the other angle will be 24x'

Now as two angles are complimentary so

x+24x=90

25x=90

x=3.6

One angle 3.6'

Other angle =24×3.6=86.4'