Let x be the measure of the angle and y be the measure of its supplementary angle.
From the given information, we have the following equation:
x = 19y
Since supplementary angles add up to 180 degrees, we also have:
x + y = 180
Substitute the first equation into the second equation:
19y + y = 180
20y = 180
y = 9
Now, substitute y back into the first equation to find x:
x = 19(9)
x = 171
Therefore, the measure of the angle is 171 degrees and the measure of its supplementary angle is 9 degrees.