SOLUTION: Find the value of x and y that will make each quadrilateral a parallelogram: upper left angle: 3y degrees lower left angle: x degrees upper right angle: (4y-65) degrees lower

Question 1002045: Find the value of x and y that will make each quadrilateral a parallelogram:
upper left angle: 3y degrees
lower left angle: x degrees
upper right angle: (4y-65) degrees
lower right angle: 3y degrees
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a parallelogram has opposite angles congruent.

upper left = lower right
lower left = upper right

you are given that:

upper left angle: 3y degrees
lower left angle: x degrees
upper right angle: (4y-65) degrees
lower right angle: 3y degrees

therefore:

3y = 3y
x = 4y-65

a parallelogram has adjacent angles supplementary.

upper left + lower left = 180
upper right + lower right = 180
upper left + upper right = 180
lower left + lower right = 180

therefore:

3y + x = 180
4y - 65 + 3y = 180
3y + 4y-65 = 180
x + 3y = 180

from 3y + 4y - 65 = 180, you can solve for y to get:
7y = 245
y = 35

if y = 35, then 3y = 105 degrees.

3y is your upper left and lower right.

the other 2 angles must be supplementary to 105 which means they must be 75 degrees and must be congruent to each other.

those two angles are your lower left and upper right.

lower left equals x degrees, so x must be equal to 75.
upper right equals 4y-65 degrees.
since y = 35, 4y-65 = 140 - 65 = 75 degrees.

it all checks out.
opposite angles are equal to each other.
adjacent angles are supplementary to each other.

this occurs when:

y = 35
x = 75

that's your solution.

the value of your angles are shown below when y = 35 and x = 75

upper left angle: 3y degrees = 3*35 = 105
lower left angle: x degrees = 75
upper right angle: (4y-65) degrees = 4*5-65 = 140-65 = 75
lower right angle: 3y degrees = 3*35 = 105

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