77.3k views
3 votes
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-example-1

2 Answers

2 votes

Answer:

Option C.

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.


6x-36=96

Add 36 on both sides.


6x-36+36=96+36


6x=132

Divide both sides by 6.


x=(132)/(6)


x=22

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

User Rashane
by
7.7k points
6 votes

Answer:

C. 22

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)°:


6x-36=96\\ \\6x=96+36\\ \\6x=132\\ \\x=22

User Mykola
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories