SOLUTION: The measures of an angle is 34 degrees less than its supplement. Find the measure of each angle.

Question 81867: The measures of an angle is 34 degrees less than its supplement. Find the measure of each angle.
Found 2 solutions by checkley75, tutor_paul:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
x+(x-34)=180
2x-34=180
2x=180+34
2x=214
x=214/2
x=107 answer for the smaller angle
proof
107+(107-34)=180
107+73=180
180=180
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
This is a problem with 2 equations and 2 unknowns. Any time you have at least as many equations as you have unknowns, you can solve the problem! The fun part is figuring out what the equations are... let A be one angle and B be the other angle. You know from the information given that the 2 angles are supplementary. 2 angles that are supplementary add up to 180 degrees. So, you can write the first equation:
Equation #1: A+B=180
You are also given the fact that one angle is 34 degrees less than the other. So you can develop another equation to reflect this:
Equation #2: A=B-34
==========================================
Now you have got your two equations and 2 unknowns, so you are good to go!
First, substitute the expression for A from Equation #2 into Equation #1:

Now that you have a value for B, substitute that into Equation #2 to find A:

You should plug these values that you found for A and B back into the original equations to see if the equations still hold true.
Good Luck,
tutor_paul@yahoo.com
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