two angles are supplementary. the measure of one angle is ten more than three times the other. find the measure of each angle.
Cindy
Let the first angle be designated as A and the second angle as B.
There are two critical pieces of information provide.
1. The two angles are supplementary. This means that they add up to 180 degrees. This can be expressed in the form of an equation: A+B=180
2. The measure of one angle is ten more than three times the other. This can be expressed in the form of a second equation: A=3B+10
We now have two equations with two unknowns. One way to solve this is by method of substitution.
We can substitute (3B+10) for A in the first equation, and solve for angle B as follows:
A+B=180
(3B+10)+B=180
3B+10+B=180
4B+10=180
4B=180-10
4B=170
B=170/4
B=42.5 degrees
We can now substitute 42.5 for B in the either of the two equations, and solve for A. Lets use the first, since that one is the simplest.
A+B=180
A+42.5=180
A=180-42.5
A= 137.5
So the value of the two angles A and B are 137.5 degrees and 42.5 degrees. Our work can be verified by plugging these values for A and B into each of the two original equations to determine if the equalities hold true with these results.
Let me know if you have any more questions.
George
