Question

What is the measure of an angle, in degrees, if its supplement is six times its complement?

Answer 1

Answer:

72 degrees.

Step-by-step explanation:

We can name the measure of the angle x.

We can name the measure of the complement of it y.

Note that complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees.

Using this info, we can set up two equations.

x+y=90

x+6y=180

Subtract the first equation from the second to eliminate x. You can do both ways, but I prefer to keep the equation positive.

x+6y=180

-x -y   -90

5y=90

Divide both sides by 5.

y=18

The complement is 18, now we can plug that in to find x.

x+18=90

Subtract 18 from both sides.

x=72

The measure of the angle is 72 degrees.