Two angles are complimentary if they sum to 90 degrees.  Two angles are supplementary if their sum is 180 degrees. To find the solution, 3 variables exist.

x: The measure of the angle

y: The measure of the supplement

z: The measure of the complement

Equations:

x+y=180 (sum of supplemental angles is 180 degrees)

x+z=90 (sum of complementary angles is 90 degrees)

y=6z (The supplementary angle is 6 times the complementary angle)

Using substitution for y, the top equation becomes x+6z=180.

Using elimination with x+6z=180 and subtracting x+z=90, the result is 5z=90 and z=18.  So the complementary angle is 18 degrees.

x=90-18=72

y=6(18)=108 or y=180-72

The solution checks when the measure of the angle is 72, the measure of the supplement is 108, and the measure of the compliment is 18.