A pair of parallel lines is cut by a transversal.

Question

A pair of parallel lines is shown cut by a transversal. Angle A is located in the upper left exterior next to the transversal, and angle B is located in the bottom right exterior corner of the transversal.

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

8
9.4
16.3
36

Answer 1

To find the value of $x$, we can use the property that angles formed by a transversal cutting parallel lines are either equal or supplementary. In this case, angles $A$ and $B$ are corresponding angles, which means they are equal.

Given: $$m\angle A=(5x-4)°$$ $$m\angle B=(8x-28)°$$

Set the two expressions equal to each other: $$5x-4=8x-28$$

Now, solve for $x$.

1. Subtract $5x$ from both sides: $$-4=3x-28$$

2. Add $28$ to both sides: $$24=3x$$

3. Divide both sides by $3$: $$x=8$$

Thus, the value of $x$ is 8.