Complementary angles add up to 90 degrees. Therefor,

x + y = 90

Supplementary angles add up to 180 degrees. Therefor,

x + z = 180

The measure of the supplement of an angle is 6 times the measure of its complement. Subtituting ‘y’ for ‘complement’, ‘z’ for ‘supplement’, and ‘=’ for ‘is’, the sentence is rewritten to: “The measure of z = 6 times the measure of y. In other words z = 6 times y.

z = 6y

Your three equations are thusly:

x + y = 90

x + z = 180

z = 6y

Between your two equations that feature ‘x’, isolate ‘x’ for one of those equations. For this example, I will leave equation 1 untouched, but will rewrite equation 2.

Equation 1: x + y = 90

Equation 2: x = 180 – z

Substitute ‘x’

180 – z + y = 90

Isolate either variable, in this case, I’ll choose ‘z’

180 + y = 90 + z

90 + y = z

Plug the newly isolated ‘z’ function into third equation and solve for ‘y’

90 + y = 6y

90 = 5y

y = 18

Substitute ‘y’ into third equation and solve for ‘z’

z = 6*(18)

z = 108

Choose either variable and plug into its respective equation, for this example I will choose the variable ‘y’ and equation 1

x + y = 90

x + 18 = 90

x = 72

Final Answer

x = 72

y = 18

z = 108

Interpret Answer

The measure of the angle is 72 degrees, the measure of its complement is 18 degrees, the measure of its supplement is 108 degrees.