Angle A and B are complementary. Their difference is 20 degrees. The smaller angle is _____ degrees.

Question

Just fill in the blank! This I found confusing because it doesn't have the total of the two angles. Once again, thanks for the help!

Answer 1

This problem is actually a system of equations. Angle A and B being complementary gives us the following equation (A + B = 90). This goes along with the second equation the difference of Angle A and B is 20 degrees (A - B = 20)

A + B = 90

A - B = 20

Adding the two equations yields the following:

2A = 110

A = 55

Substituting back into the first equation:

55 + B = 90

B = 90 - 55

B = 35

The final step is substitute your answers for A & B into both equations to make sure they are both correct.

55 + 35 = 90

55 - 35 = 20

The smaller angle is 35 degrees.

Answer 2

The smaller angle is 35 degrees.

This is because the sum of complementary angles is 90 degrees. We will denote angle B as x, which makes angle A as x + 20. This gives us the following equation:

x + (x + 20) = 90

2x + 20 = 90

2x + 20 - 20 = 90 -20

2x = 70

x = 35

Since we denoted x as angle B, the value of angle B is 35 degrees. A is denoted as x + 20, so its angle value is (35 + 20) = 55 degrees.

We can check that 35 degrees + 55 degrees indeed equals 90 degrees.