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Parallelograms
A
B
C
D
E
. . . .

Properties of Parallelograms (2)

Example 3

Find the values of the variables in the parallelogram.


Solution

Since S and U are adjacent in parallelogram SURE,

mS+mU = 180
x+ 65 = 180
x = 180 65
= 115 .

Since U and E are opposite angles, EU. Hence,

mE =mU
z 5 = 6
z = 70 .

Moreover, S and R are opposite angles. Therefore, RS. It follows that

mR =mS
y+ 19 = 115
y = 96 .

Thus, x= 115 ,y= 86 , and z= 70 .