Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 4 = 51 ^ { circ } ). find ( m angle 5 ) and ( m angle 7 ).

Explanation:

Step1: Find \( m\angle5 \)

Since \( \angle4 \) and \( \angle5 \) are alternate interior angles, and when two parallel lines are cut by a transversal, alternate interior angles are congruent.
So \( m\angle5=m\angle4 = 51^{\circ}\)

Step2: Find \( m\angle7 \)

Since \( \angle5 \) and \( \angle7 \) are vertical angles, and vertical angles are congruent.
So \( m\angle7=m\angle5 = 51^{\circ}\)

Answer:

\( m\angle5 = 51^{\circ}\), \( m\angle7 = 51^{\circ}\)