Complemetary angles are two angles whose measures add up to 90 degrees. The ratio of the measures of two complementary angles is 2:13. What are the measures of the angles?

Let A and B be the two complementary angles.

A = smaller angle = 2x

B = larger angle = 13x

x = some unknown number

Note how the ratio A:B turns into 2x:13x which simplifies to 2:13

A+B = 90 ... because the angles are complementary

2x+13x = 90 ... substitution

15x = 90

x = 90/15

x = 6

A = 2*x = 2*6 = 12 degrees

B = 13*x = 13*6 = 78 degrees

The two angles are 12 degrees and 78 degrees.

Check:

A/B = 12/78 = (2*6) / (13*6) = 2/13, so A:B = 2:13

A+B = 12+78 = 90