Answer:
a. 42, 48
Explanation:
The angles being complementary means their total measure is 90°.
(12q -9) +(8q +14) = 90
20q +5 = 90 . . . . . . . . . . . simplify
20q = 85 . . . . . . . . . . . . . . subtract 5
q = 4.25 . . . . . . . . . . . . . . . divide by 20
Now, put this value into the expressions for the angle measures:
12q -9 = 12·4.25 -9 = 42
8q +14 = 8·4.25 +14 = 48
These two angle measures total 90, so our answer checks OK.
The measures of the angles are 42 and 48 degrees.