SOLUTION: The sum of two angles' measures is 95 degrees. Angle 2 is 105 degrees smaller than 3 times angle 1. What are the measures of the two angles in degrees?

Question 624368: The sum of two angles' measures is 95 degrees. Angle 2 is 105 degrees smaller than 3 times angle 1.
What are the measures of the two angles in degrees?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Let's call the two angles A and B instead of angle 1 and 2 because we want to use their names as variables.

So
"The sum of two angles' measures is 95 degrees."
translates into
A + B = 95

"Angle 2 is 105 degrees smaller than 3 times angle 1"
translates into
B = 3*A - 105

With two variables and two equations we have a system we can solve. Since the second equation is already solved for B, using the Substitution Method might be easiest. Using the expression for B in the second equation we can substitute for the B in the first equation:
(3*A - 105) + A = 95
(Note the use of parentheses. It is always a good idea to use parentheses when substituting one expression for another.)
Simplifying the left side:
4A - 105 = 95
Adding 105 to each side:
4A = 200
Dividing both sides by 4:
A = 50

To find B we use the value we just found for A and either of the earlier equations. Using the first equation:
(50) + B = 95
Subtracting 50:
B = 45

So angle 1 is 50 degrees and angle 2 is 45 degrees.
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