Question

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.

Explanation:

Step1: Use the Basic Proportionality Theorem (Thales' theorem) for parallel lines cut by transversals. The theorem states that if three or more parallel lines are cut by two transversals, the segments are proportional. So we set up the proportion: $\frac{42}{52}=\frac{x}{23}$

Step2: Cross - multiply to solve for $x$. Cross - multiplying gives us $52x = 42\times23$. First, calculate $42\times23 = 966$. Then, solve for $x$ by dividing both sides of the equation by 52: $x=\frac{966}{52}$

Step3: Simplify the fraction $\frac{966}{52}$. Dividing 966 by 52 gives $x\approx18.6$ (rounded to the nearest tenth)

Answer:

$18.6$