Answer:
C. x = 50, y = 10
Explanation:
This is another case where the majority answer is correct.
x=50 appears more times than any other value.
y=10 appears more times than any other value.
Trying these values in the given expressions makes the angles be 150° and 30°. Vertical angles are equal and adjacent angles are supplementary, as they should be.
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Multiple-choice questions are as much about "test-taking skill" as they are about solving math problems. Often, the correct choice will appear in various forms in the different answer choices, so it can sometimes work to select the number(s) that appear(s) most often. In any event, it is usually a simple matter to check to see if those numbers solve the problem.
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If you want to work the problem, not just check answers ...
Adjacent angles are supplementary, so you have two equations, one for x and one for y:
(5x -100)° +(x -20)° = 180°
6x -120 = 180 . . . . collect terms, divide by °
x -20 = 30 . . . . . . . divide by 6
x = 50 . . . . . . . . . . .add 20
and for y ...
(3y)° + (y+140)° = 180°
4y +140 = 180 . . . . . . . divide by °, collect terms
y +35 = 45 . . . . . . . . . .divide by 4*
y = 10 . . . . . . . . . . . . . . subtract 35
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* It can be easier to subtract 140 before dividing by 4. The subtraction is easy and results in 40, which is easily divided by 4. 140/4 and 180/4 are not particularly easy quotients to find mentally (though dividing by 2 twice is a decent strategy).