how do I solve for the measurment of a?

Question

<a and <b are complementary angles. If m<a=(2x+27) degrees and m<B=(2x-21) degrees, then find the measurement of a.

Answer 1

The answer is 72.5 degrees. Complementary angles are angles which add to 90 degrees. Therefore, you can algebraically solve this problem as follows:

(2x+20)+(2x-21) = 90

combine like terms to get 4x -1 = 90

add 1 to each side to get 4x = 91

91/4 = x

and since angle a is 2x + 27 this means it is 2(91/4) + 27 or 72.5 degrees.

Angle B is 2(91/4)-21 or 24.5 degrees, which checks out since angles A and B therefore add to 90 degrees and are complementary.