Question

HELP pls!!

Answer 1

Answer: Choice B) x = 65, y = 10

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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

$\ \ \ 2x-y = 120\\+ 2x+y = 140\\\hrule\\\\\\ \ \ \ 4x+0y = 260$

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