The measure of a supplement of an angle is 6 times the measure of the complement of the angle. Find the measure of the angle, its supplement, and...

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.