Question

quiz 4: p the value of m is: 14, 18, 20, 28 (with a diagram of parallel lines and transversals showing segments 8, 6, 21 and m)

Explanation:

Step1: Identify the theorem

This is a problem about parallel lines cut by transversals, so we use the Basic Proportionality Theorem (Thales' theorem) which states that if three or more parallel lines are cut by two transversals, then they divide the transversals proportionally. So, we set up the proportion $\frac{8}{m}=\frac{6}{21}$.

Step2: Solve for \( m \)

Cross - multiply the proportion: \( 6\times m = 8\times21 \).
First, calculate \( 8\times21 = 168 \). Then, we have the equation \( 6m=168 \).
Divide both sides of the equation by 6: \( m=\frac{168}{6}=28 \).

Answer:

28