On our math test, I made two complementary angles; one of the angles is 26 ̊more than the other. Identify the angles.

So,

Let x represent the first angle and y represent the second angle.

x + y = 90

x = y + 26

Substitute

y + 26 + y = 90

Collect Like Terms

2y + 26 = 90

Subtract 26 from both sides

2y = 64

Divide both sides by 2

y = 32

Substitute

x = 32 + 26

x = 58

Check

58 + 32 = 90

90 = 90 This checks.

58 = 32 + 26

58 = 58 This also checks.

The measure of one angle is 58° and the measure of the other angle is 32°.