Given that a transversal cuts two parallel lines and forms angles such that $m\angle 4$ = $55.1°$, what are the measures of $m\angle 5$ and $m\angle 7$?

• A. $m\angle 5$ = $55.1°$, $m\angle 7$ = $124.9°$
• B. $m\angle 5$ = $124.9°$, $m\angle 7$ = $55.1°$
• C. $m\angle 5$ = $124.9°$, $m\angle 7$ = $124.9°$
• D. $m\angle 5$ = $90°$, $m\angle 7$ = $55.1°$

Answer: (B)

Verified step by step guidance

1. Identify the relationship between the angles formed by the transversal cutting two parallel lines. Recall that alternate interior angles are equal, corresponding angles are equal, and consecutive interior angles are supplementary (sum to 180°).
2. Given that \(m\angle 4 = 55.1^\circ\), determine which angles are congruent or supplementary to \(\angle 4\) based on their positions relative to the parallel lines and the transversal.
3. Use the property of supplementary angles to find \(m\angle 5\). Since \(\angle 4\) and \(\angle 5\) are consecutive interior angles, their measures add up to 180°, so write the equation: \(m\angle 4 + m\angle 5 = 180^\circ\).
4. Solve the equation for \(m\angle 5\) by subtracting \(m\angle 4\) from 180°, i.e., \(m\angle 5 = 180^\circ - m\angle 4\).
5. Determine \(m\angle 7\) by identifying its relationship to \(\angle 4\) or \(\angle 5\). If \(\angle 7\) is alternate interior or corresponding to \(\angle 4\), then \(m\angle 7 = m\angle 4\). Otherwise, use supplementary or vertical angle relationships to find its measure.