A pair of parallel lines is cut by a transversal. If m∠A = (5x − 4)° and m∠B = (8x − 28)°, what is the value of x?

Question

A pair of parallel lines is cut by a transversal.

If m∠A = (5x − 4)° and m∠B = (8x − 28)°, what is the value of x?

1. 8 
2. 9.4 
3. 16.3 
4. 36

Answer 1

For this question, the first step would be to identify that A and B are alternate exterior angles, meaning they are equivalent.

So, since A = B, we can set up the algebraic equation: 5x - 4 = 8x - 28.

I will let you solve from there.

Remember that the crucial thing to understand in the problem is that A & B are alternate exterior angles, and that you can set them equal to each other.

Answer 2

Angles A and B are alternate exterior angles. I presume that you are a Geometry student, so you need to become familiar with the terms involved.

We are given that the lines are parallel, and the consequence here is that angles A and B are congruent, meaning that they have equal measures.

Thus, 5x-4 = 8x-28.

Adding 28 to both sides and subtracting 5x from both sides of the above equation results in

24 = 3x

Dividing both sides by the coefficient of the variable x

8 = x

So the correct answer choice is 1. Since the degree mark is on the outside of the parentheses, x has no degrees and is "unitless".