Question Help Find the measure of an angle such that the difference between the measures of its supplement and six times its complement is 10​°

Question

I'm needing help setting this one up

Answer 1

Let X be this mysterious angle.

 

The complement is (90-x)

 

The supplement is (180 -x)

 

The difference between the supplement and 6 times the complement is 10

 

                            (180 - x) -6(90-x) = 10

                             180 - x - 540 + 6x = 10 <--- distributes -6

 

                          5x - 360 = 10  <--- combines like terms

 

                               5x = 370  <--- solves for x

 

                                x = 370/5 = 74

 

The angle is 74.

The complement is 90 - 74 = 16.

The supplement is 180 - 74 = 106.

 

106 - 6(16) = 106 - 96 = 10 <--- yes it works!!!

 

The angle is 74, the answer is checked, verified, and proven to be correct.