Question

two parallel lines are crossed by a transversal. what is the value of m? diagram: two parallel lines e (top) and f (bottom) with transversal d. angle between d and e is 78°, angle between d and f is m°. options: m = 68, m = 78, m = 102, m = 112

Explanation:

Step1: Identify angle relationship

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^\circ\)). The \(78^\circ\) angle and \(m^\circ\) are consecutive interior angles.

Step2: Set up equation

\(78 + m = 180\)

Step3: Solve for \(m\)

\(m = 180 - 78 = 102\)

Answer:

\(m = 102\) (corresponding to the option \(m = 102\))