Question

in exercises 3–8, find the valu explain your reasoning. (see 3. image of two parallel lines m and n cut by a transversal, with a 120° angle and a 3x° angle as shown)

Explanation:

Step1: Identify angle relationship

Lines \( m \) and \( n \) are parallel, and the transversal creates alternate interior angles (or corresponding, since \( 120^\circ \) and \( 3x^\circ \) are equal as they are alternate interior angles for parallel lines). So \( 3x = 120 \).

Step2: Solve for \( x \)

Divide both sides by 3: \( x=\frac{120}{3}=40 \).

Answer:

\( x = 40 \)