If the complement of an angle is one-tenth of the supplement of the angle, find the measure of the angle.

Question

I need help setting up the equation to find the end product please?

Answer 1

 

The complement of an angle is the difference between 90 degrees and the angle.  The supplement of an angle is the difference between 180 degrees and the angle.

 

Let          x = the angle

Let   90 - x = the complement

Let 180 - x = the supplement

 

Since the complement is 1/10th of the supplement, we have this equation:

 

   90 - x = .1(180 - x)

   90 - x = 18 - .1x

   90 = 18 - .1x + x

   90 - 18 = .9x

   72 = .9x

   72/.9 = .9x/.9

   80 = x

 

The angles is 80 degrees.

 

CHECK:

The complement is 10 degrees.

The supplement is 100 degrees.

10 is 1/10th of 100.