Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle 5 = 41^circ ). find ( mangle 2 ) and ( mangle 4 ).

Explanation:

Step1: Find \( m\angle 2 \)

Since the two lines are parallel and cut by a transversal, \( \angle 2 \) and \( \angle 5 \) are alternate interior angles. Alternate interior angles are equal when the lines are parallel. So \( m\angle 2 = m\angle 5 \). Given \( m\angle 5 = 41^\circ \), then \( m\angle 2 = 41^\circ \).

Step2: Find \( m\angle 4 \)

\( \angle 4 \) and \( \angle 2 \) are supplementary angles (they form a linear pair). The sum of supplementary angles is \( 180^\circ \). So \( m\angle 4 + m\angle 2 = 180^\circ \). Substituting \( m\angle 2 = 41^\circ \), we get \( m\angle 4 = 180^\circ - 41^\circ = 139^\circ \).

Answer:

\( m\angle 2 = \boxed{41}^\circ \)
\( m\angle 4 = \boxed{139}^\circ \)