The measure of two supplementary angles are 12q-9 and 8q+14 find the measures of the angles

First choose 1 equation and set it equal to 180 because supplementary angles equal up to 180 degrees. 

12q - 9 =180                                                              

Now solve for q.

12q - 9 +9 = 180 + 9

12q = 189

12q/12 = 18912

q = 15.75

now subtract 15.75 from 180

180.00 - 15.75 = 164.25

Your angles equal to 164.25 and 15.75 degrees.

The answer is 60.9774