Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Since the two vertical lines are parallel, the angle with measure $123^{\circ}$ and the angle with measure $(4x - 3)^{\circ}$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent.

Step2: Set up the equation

We set up the equation $4x-3 = 123$.

Step3: Solve for x

Add 3 to both sides of the equation: $4x-3 + 3=123 + 3$, which simplifies to $4x=126$. Then divide both sides by 4: $x=\frac{126}{4}=\frac{63}{2}=31.5$.

Answer:

$x = 31.5$