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## math problem

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

Hi Cindy;
x...first angle
3x+10...second angle

(x)+(3x+10)=180
x+3x+10=180
Let's combine like terms...
4x+10=180
Let's subtract 10 from both sides...
4x=170
Let's divide both sides by 4...
x=42.5
3x+10=137.5

If the angles are supplementary, that means that the sum of the two angles is 180 degrees.  Make one angle "x."  The other angle is 10 more than 3 times "x".  When both "x" and 10 more than 3 times "x" are added together, their sum is 180 degrees.

Times means multiply so 3 times "x" is 3x.  More than means add.  From there, you should be able to write an equation in terms of "x" to solve.