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Lines a and b are cut by transversal f. At the intersection of lines f and a, the top left angle is 96 degrees. At the intersection of lines b and f, the bottom right angle is (6 x minus 36) degrees.
What must be the value of x so that lines a and b are parallel lines cut by transversal f?

10
20
22
32

Lines a and b are cut by transversal f At the intersection of lines f and a the top left angle is 96 degrees At the intersection of lines b and f the bottom rig class=

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frika

Answer:

C. 22

Step-by-step explanation:

Inverse Alternate Interior Angles Theorem sttes that if two lines a and b are cut by transversal f so that the alternate interior angles are congruent, then a║b.

To prove that lines a and b are parallel, equate the measures of angles 96° and (6x-36)°:

[tex]6x-36=96\\ \\6x=96+36\\ \\6x=132\\ \\x=22[/tex]

Answer:

Option C.

Step-by-step explanation:

It is given that lines a and b are cut by transversal f.

If a transversal line intersect two parallel lines, then the alternate exterior angles are same.

We need to find the value of x so that lines a and b are parallel lines cut by transversal f.

So, equate both alternate exterior angles.

[tex]6x-36=96[/tex]

Add 36 on both sides.

[tex]6x-36+36=96+36[/tex]

[tex]6x=132[/tex]

Divide both sides by 6.

[tex]x=\frac{132}{6}[/tex]

[tex]x=22[/tex]

The value of x is 22. Therefore, the correct option is C.

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