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Work Shown:
The upper pair of angles 60 degrees and (2x-y) degrees are supplementary angles. This is because of the parallel lines. Note how they are same side interior angles. Therefore, (2x-y) and 60 combine to 180 degrees like so
(2x-y)+60 = 180
2x-y = 180-60 ... subtract 60 from both sides
2x-y = 120 ... call this equation 1
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Similarly, (2x+y) and 40 also combine to 180
(2x+y) + 40 = 180
2x+y = 180-40 ... subtract 40 from both sides
2x+y = 140 ... call this equation 2
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Line up equation 1 and equation 2. Then add straight down
That becomes 4x = 260 which solves to x = 65 when you divide both sides by 4.
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If x = 65, then,
2x-y = 120
2(65)-y = 120
130 - y = 120
-y = 120-130
-y = -10
y = 10
or
2x+y = 140
2(65)+y = 140
130+y = 140
y = 140-130
y = 10
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Either way end up with x = 65 and y = 10
