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Find the value of x x, y y, and z z in the parallelogram below.

Find The Value Of X X Y Y And Z Z In The Parallelogram Below class=

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Upandoveridn

In a parallelogram, angles that are opposite each other (as in, in opposite corners) are congruent. Angles that are next to each other (as in, on the same side) are supplementary.

It is very easy to solve for the value of y first because the expression is across from a known angle. Because these angles are opposite each other, they are congruent.

83 = 5y - 7

90 = 5y

y = 18

We can also use the same 83 degree angle to solve for the other two variables. 83 is on the same side as both of the remaining expressions, separately. As such 83 and another angle on the same side will add up to 180.

83 + -5x - 3 = 180

80 - 5x = 180

-5x = 100

x = -20

83 + z - 7 = 180

90 + z = 180

z = 90

Hope this helps!

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