SOLUTION: Problem Solving With Systems of A line: How to Solve The difference of the measures of two supplementary angles is 35*. Find both angle measures. The sum they add up to is 180*.

SOLUTION: Problem Solving With Systems of A line: How to Solve The difference of the measures of two supplementary angles is 35. Find both angle measures. The sum they add up to is 180.

Question 123811: Problem Solving With Systems of A line: How to Solve
The difference of the measures of two supplementary angles is 35*. Find both angle measures. The sum they add up to is 180*.
Found 2 solutions by bucky, eschwartz:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let mA represent the measure of angle A and let mB represent the measure of the angle B.
.
If the two angles are supplementary then the sum of their measures is 180 degrees. This can be
written in equation form as:
.
mA + mB = 180
.
But the problem also tells you that the difference in their measures is 35 degrees. In
equation form this could be written as:
.
mA - mB = 35
.
Solve this equation for mA by getting rid of mB on the left side. You can get rid of mB on
the left side by adding mB to both sides. On the left side the -mB plus the mB that is added
cancel each other. On the right side you add the mB and as a result the equation becomes:
.
mA = 35 + mB
.
Return to the supplementary equation and for mA substitute its equivalent form 35 + mB.
The supplementary equation is:
.
mA + mB = 180
.
Replacing mA with 35 + mB makes the equation become:
.
35 + mB + mB = 180
.
Combine the mB terms to get 2*mB and this makes the equation:
.
35 + 2*mB = 180
.
Get rid of the 35 on the left side by subtracting 35 from both sides. This makes the equation
become:
.
2*mB = 180 - 35 = 145
.
Since 2*mB = 145 you can solve for mB by dividing both sides of this equation by 2 to get:
.
mB = 145/2 = 72.5
.
This tells you that the measure of angle B is 72.5 degrees.
.
And since mA + mB = 180 degrees, if we replace mB by 72.5 degrees, the equation becomes:
.
mA + 72.5 = 180
.
Get rid of the 72.5 degrees on the left side by subtracting 72.5 from both sides. This
reduces the equation to:
.
mA = 180 - 72.5 = 107.5
.
So the measure of the second angle is 107.5 degrees.
.
The measures of the 2 angles are mA = 107.5 degrees and mB = 72.5 degrees.
.
Hope this helps you to understand the problem.
.

Answer by eschwartz(9) (Show Source): You can put this solution on YOUR website!
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