SOLUTION: the measurement of angle 1 =2x+40
the measurement of angle 2 =2y+40
the measurement of angle 3 =x+2y
And there is a picture that looks roughly like this:
('e's are used to prov
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Question 557102: the measurement of angle 1 =2x+40
the measurement of angle 2 =2y+40
the measurement of angle 3 =x+2y
And there is a picture that looks roughly like this:
('e's are used to provide correct spacing
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eeeeee1e\ee2
<-------------------->
eeeeeeeeee\ 3
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Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Angles 1 and 3 are vertical to each other; angle 2 is supplementary to 1 and to 3.
(angles 1 and 3 have the same measure)
(measures of angles 1 and 2 add to 180°)
(measures of angles 2 and 3 add to 180°)
That gives you 3 equations on 2 variables.
Let's simplify:
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--> --> -->
--> -->
With two of the equations we may find a solution, which we would need to substitute in the other equation to see that it verifies.
If we take the system
subtracting the first equation from the second, we get
-->
and substituting into the first equation we get
-->
If with satisfies , then (x,y)=(20,30) is the solution. If not, there is no solution.
With and , , so (20,30)
(or with ) is the solution.
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