Answers:
x = 13 and y = 11
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Step-by-step explanation:
Check out the diagram below. I've added in the label (4x+13) degrees to the angle adjacent to the (9x-2) degree angle. This is valid due to corresponding angles being congruent when we have parallel lines like this.
The two angles form a 180 degree straight angle
(4x+13) + (9x-2) = 180
4x+13 + 9x-2 = 180
(4x+9x) + (13-2) = 180
13x + 11 = 180
13x+11-11 = 180-11 .... subtracting 11 from both sides
13x = 169
13x/13 = 169/13 .... dividing both sides by 13
x = 13
We can verify this by noticing that
4x+13 = 4*13+13 = 65
9x-2 = 9*13-2 = 115
So, (4x+13)+(9x-2) = (65)+(115) = 180, showing the two angles are supplementary.
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The angles (9x-2) and (6y-1) are also a linear pair. They are adjacent and supplementary
Let's use x = 13 to find the value of y
(9x-2) + (6y-1) = 180
9x-2+6y-1 = 180
9x+6y-3 = 180
9*13+6y-3 = 180 .... plug in x = 13
117+6y-3 = 180
6y+114 = 180
6y+114-114 = 180-114 .... subtract 114 from both sides
6y = 66
6y/6 = 66/6 ...... divide both sides by 6
y = 11
To help confirm,
6y-1 = 6*11-1 = 65
which adds onto the (9x-2) = 115 degree angle to get 180.
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Side note: as an alternative, you can solve 4x+13 = 6y-1 to get the same y value. This is because alternate exterior angles are congruent when we have parallel lines like this.