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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,

m∠S+m∠U = 180 ∘
x+ 65 ∘ = 180 ∘
x = 180 ∘ − 65 ∘
= 115 ∘ .

Since ∠U and ∠E are opposite angles, ∠E≅∠U. Hence,

m∠E =m∠U
z− 5 ∘ = 6 ∘
z = 70 ∘ .

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

m∠R =m∠S
y+ 19 ∘ = 115 ∘
y = 96 ∘ .

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