9514 1404 393
Answer:
d. z = -48
Explanation:
When j ║ k, corresponding angles are congruent, so ...
x = 4z +3y
57 = y + z
and the same-side interior angles are supplementary:
57 +x = 180 ⇒ x = 123
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This lets us write two equations in y and z:
3y +4z = 123
y +z = 57
Using the second equation to write an expression for y, we have ...
y = 57 -z
Substituting this into the first equation gives ...
3(57 -z) +4z = 123
z +171 = 123
z = -48 . . . . . . . subtract 171
The value of z that makes j║k is -48.
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The corresponding value of y is 105.