Question

two parallel lines are crossed by a transversal. what is the value of b? diagram: lines m (transversal), p (top, horizontal), q (bottom, horizontal) with arrows indicating parallelism. angle ( b^circ ) is formed between transversal m and line p; a ( 128^circ ) angle is formed between transversal m and line q. options: ( b = 32 ), ( b = 52 ), ( b = 118 ), ( b = 128 )

Explanation:

Step1: Identify angle relationship

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^\circ\)). Here, \(b^\circ\) and \(128^\circ\) are consecutive interior angles.

Step2: Set up equation

\(b + 128 = 180\)

Step3: Solve for \(b\)

\(b = 180 - 128\)
\(b = 52\)

Answer:

\(b = 52\) (corresponding to the option "b = 52")