Question 133115
As soon as you see the word complementary, you must know that the angles add up to 90 degrees.

angle A + angle B = 90

angle A = 9 less than TWICE angle B. We don't know what angle B is, right? I will say that angle B = x.

angle A = 2x - 9

We now have this equation:

2x - 9 + x = 90

Solve for x.

3x - 9 = 90

3x = 90 + 9

3x = 99

x = 99/3

x = 33

The measure of angle A = 2(33) - 9.

angle A = 66 - 9

angle A = 57 degrees

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angle B = x and I just found that x = 33, right?

Then, angle B = 33 degrees.

How do you know that I am right?

When adding 33 + 57, I get 90 degrees ON BOTH SIDES of the equation.

Did you follow?

NOTE: If you see a similar question saying that two angles are supplementary, this means that both angles, when added, will produce 180 degrees.  I give you this information now because most likely you will a question like that in your math course.