Question

The measures of complementary angles have a sum of 90 degrees.Angle A and angle B are complimentary, and their measures have a difference of 20 degrees.What are the measures of the angles?

Answer 1

To find the measures of the two complementary angles, we set up two equations based on their sum (90 degrees) and their difference (20 degrees). Solving these equations, we find that angle A measures 35 degrees and angle B measures 55 degrees.

Step-by-step explanation:

The measures of complementary angles have a sum of 90 degrees. If one angle is 20 degrees more than the other, let's call the smaller angle A and the larger angle B. Since they are complementary, we can write two equations:

1. A + B = 90 (because they are complementary)
2. B - A = 20 (given in the question, the difference between the two angles)

Adding the two equations, we get:

2B = 110

So, B = 55 degrees. Substituting B in the first equation, we get A + 55 = 90, therefore A = 35 degrees. Angle A measures 35 degrees and angle B measures 55 degrees.

Answer 2

The measure of the angles are 55° and 35°

Step-by-step explanation:

Sum of two angles that are complement of each other are 90.

The angles are A and B, so we can write:

A + B = 90

Also,

The difference is 20. Let A be the greater of them, so we can write equation 2 as:

A - B = 20

Now, we add up both equations, eliminate B and solve for A first:

A + B = 90

A - B = 20

---------------

2A = 90 + 20

2A = 110

A = 110/2

A = 55

And now the measure of B:

A + B = 90

55 + B = 90

B = 90 - 55

B = 35