Question

The difference of 2 complementary angles is 12. Find the measure of the angles.

Answer 1

If two angles are complementary, the sum of their measures is 90 degrees.
Call one of the angles x.
This means that its complement is (90 - x) degrees.
But the difference in their measures is 12 degrees. Therefore, you can write the equation:
x - (90 - x) = 12

Since the parentheses are preceded by a minus sign, you can remove the parentheses if you also
change the signs of the terms inside the parentheses. Therefore, when you remove the parentheses
the equation becomes:
x - 90 + x = 12

Combine the two x terms on the left side to get:

2x - 90 = 12

Get rid of the -90 on the left side by adding 90 to both sides to get:
2x = 102

Solve for x by dividing both sides of the equation by 2 to get:

x = 102/2 = 51

So the measure of one of the two angles is 51 degrees. Its complement is the amount that
must be added to that angle such that this sum is 90 degrees. By subtracting 51 from 90
degrees, you find that the complement of the angle is an angle of 39 degrees. Note that
the difference in the two angles is 51 - 39 = 12 degrees, just as the problem specified.

The answer to this problem is that the measures of the two complementary angles are
51 degrees and 39 degrees.