How large is an angle whose supplement is 21 degrees less than 4 times its complement?

Question

It's an Algebra II geometry problem- involving suplementary and complementary angles. Help?

Answer 1

The angle is x.  The supplement is 180 - x because supplementary angles add up to 180. The complement is 90 - x.  So we have:

 

(180 - x) = 4(90 - x) - 21

the supplement  is  4 times the complement minus 21

 

Solve for x:

180 - x = 360 - 4x - 21

180 - x + 4x = 360 - 21

3x = 360 - 21 - 180

3x = 159

x = 159/3

x = 53

Answer 2

Let x = angle.

Then,

      (180° - x) is the supplement

      (90° - x) is the complement

 

Translate:

"supplement is 21 degrees less than 4 times its complement"

  (180° - x)    =     -21°           +       4    *    (90° - x)

 

The math:

   180°  - x = 360° - 21° - 4x

           3x = 159°

           x = 53°

 

Check:

      Supplement        is         4*Complement - 21°

              127°           =          4(37°) - 21°

              127°           =          127°

    O.K.