Hi, there--

Problem:
Find the measure of an angle that is four hundred twenty less than three times its supplement.

A Solution:

Let a be the measure of the angle.

Two angles are supplementary if their sum is 180. Thus the supplement of the angle is
180-a.

"Three times the supplement" is 3*(180-a).

"Four hundred twenty less than three times the supplement" is 3*(180-a) - 420.

Altogether we have 
a = 3*(180-a) - 420

Now simplify using the distributive property.
a = 540 - 3a - 420

Combine like terms.
a = -3a + 120

Add 3a to both sides of the equation.
4a = 120

Divide both sides of the equation by 4.
a = 30

In the context of this problem, a=30 means that the measure of the angle is 30 degrees.

Let's check our calculations with the original sentence.

The supplement of a 30 degree angle is 150 degrees because 30+150=180.
Three times the supplement is 3*150, or 450 degrees.

Four hundred twenty less than 450 degrees IS 30 degrees because 450-420=30. Check!


Good luck!
Mrs. Figgy