If the ratio of the measures of two complementary angles is 3 to 2 then what is the measure of each angle?

Two complementary angles, let's call them A & B, when added together = 90 degrees. We also know that the ratio of angle A to angle B is 3:2. Using some basic algebra we can solve for each angle. We know that A + B = 90 (since the angles are complementary). We also know that A/B = 3/2. Cross-multiplying, we get 2A = 3B. Solving for A, we get A = 3B/2. So, substituting for A into the first equation, we get (3B/2) + B = 90. If we multiply both sides of the equation by 2, we get 3B + 2B = 180. So, 5B = 180. Solving for B yields B = 36. Since A + B = 90, we know that A = 90 - B = 90 - 36 = 54. Does that answer make sense? Let's check. Does 54/36 equal 3/2? Reducing 54/36 to lowest terms yields 3/2. Nice. So, A = 54 degress and B = 36 degrees.

Let the angles be 3x and 2x.

Both the angles are complementary angles.

Complementary angles are two acute angles that add up to give a right angle, 90°.

2x + 3x = 90

5x = 90

x = 18.

2x = 2(18) = 36

3x = 3(18) = 54

Complementary angles are angle pairs whose measures add up to 90 degrees.