Question

two parallel lines are crossed by a transversal. what is the value of k? k = 9, k = 20, k = 60, k = 71

Explanation:

Step1: Identify angle relationship

Since lines \( y \) and \( z \) are parallel, and \( x \) is a transversal, the angle \( (2k + 11)^\circ \) and \( 131^\circ \) are corresponding angles (or alternate interior angles, depending on the diagram), so they are equal. Thus, we set up the equation:
\( 2k + 11 = 131 \)

Step2: Solve for \( k \)

Subtract 11 from both sides:
\( 2k = 131 - 11 \)
\( 2k = 120 \)

Divide both sides by 2:
\( k = \frac{120}{2} \)
\( k = 60 \)

Answer:

\( k = 60 \) (corresponding to the option \( k = 60 \))