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Question 249410: How do i solve this (Two angles are supplementary. One angle measures 26 degrees more than the other one. Find the measure of the two angles.)
Found 2 solutions by richwmiller, chosenpoint:
Answer by richwmiller(17219)   (Show Source):
Answer by chosenpoint(26)  (Show Source):
You can put this solution on YOUR website! Supplementary angles are a pair of angles which add up to 180 degrees.
Usually, these are angles that share a side and make up a straight line, but they do not have to be adjacent to be supplementary.
The only thing that matters is that they add up to 180 degrees.
Let x be the first unknown angle.
Then our second angle has to equal 180-x by definition, thus we can use the given info about the measure of the angles, and we know that:
x+26=180-x or that x=180-x+26
We will start with the first supposition:
x+26=180-x given
2x=180-26 add x to both sides
2x=154 simplify
x=77 so 180-x=103 final answer
Second supposition:
x=180-x+26 given
2x=206 add x to both sides and simplify
x=103 so 180-x=77 final answer
In either case, it is easy to see that the large angle is 103 degrees, which is bigger than the smaller angle of 77 degrees.
The larger angle measures 26 degrees greater than the smaller angle, which is what we were looking for, and we can also see that the sum of the two angles is 180 degrees, which by definition, makes them supplementary! Hope that helps.
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