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

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)°:

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.

Add 36 on both sides.

Divide both sides by 6.

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