If the complement of angle is 6 degrees less than one-fourth its supplement find the measure of the angle

Question

please help this problem got my head spinning, i cant seem to even find an equation for it

help help  

Answer 1

Let x = the angle

 

The complement of the angle = 90° - x

 

The supplement of the angle = 180° - x

 

So, 90 - x = (1/4)(180 - x) - 6

 

Multiply the equation by 4 to get 360 - 4x = 180 - x - 24

                                                          360 - 4x = 156 - x

                                                                  204 = 3x

                                                                       x = 68°