Two angles are supplementary if they add up to 180 degrees.

Let 'x' and 'y' represent the angles

since x and y are supplementary we have:

x + y = 180

the measure of one angle is 9 degrees more than twice the measure of the other:

x = 9 + 2y

by solving the system of equations:

x + y = 180

x = 9 + 2y

we find:

x = 123 degrees

y = 57 degrees

click here to see the step by step solution of the system of equations:

the measures of the angles are: 123 degrees and 57 degrees.