given lines $l$, $m$, and $n$ are parallel and cut by two transversal lines, find the value of $x$. round…

given lines $l$, $m$, and $n$ are parallel and cut by two transversal lines, find the value of $x$. round your answer to the nearest tenth if necessary.

given lines $l$, $m$, and $n$ are parallel and cut by two transversal lines, find the value of $x$. round your answer to the nearest tenth if necessary.

Answer

Explanation:

Step1: Identify the geometric theorem

Parallel lines intersecting transversals create proportional segments.

Step2: Set up the proportionality equation

Based on the Parallel Lines Proportionality Theorem: $$\frac{x}{24} = \frac{20}{40}$$

Step3: Simplify the ratio

Reduce the fraction on the right side: $$\frac{x}{24} = \frac{1}{2}$$

Step4: Solve for $x$

Multiply both sides by $24$: $$x = 24 \cdot \frac{1}{2}$$ $$x = 12$$

Answer:

12