Answers: x = 13 and y = 11
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Let's focus on the angle expressions that have x in them.
They are adjacent angles and they form a straight line. So we consider them a linear pair. All linear pair angles always add to 180
(3x+89)+(7x-39) = 180
(3x+7x) + (89-39) = 180
10x+50 = 180
10x = 180-50
10x = 130
x = 130/10
x = 13
We'll use the same idea to find y
(3y+19)+(4y+84) = 180
(3y+4y) + (19+84) = 180
7y+103 = 180
7y = 180-103
7y = 77
y = 77/7
y = 11
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Extra info (optional section)
Let's find the measures of the four angles based on the x and y values we found.
- 3x+89 = 3*13+89 = 128
- 7x-39 = 7*13-39 = 52
- 3y+19 = 3*11+19 = 52
- 4y+84 = 4*11+84 = 128
It's not a coincidence that the 3x+89 and 4y+84 angles are equal (to 128). These are vertical angles which are always congruent. The other pair of congruent vertical angles are the 3y+19 and 7x-39 angles.
Note how 128+52 = 180 to help further confirm we have the correct values.
Another thing to notice is that all four angles add up to 360 degrees.