Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle 2 = 103^{circ} ). find ( mangle 5 ) and ( mangle 7 ). ( mangle 5=square^{circ} ) ( mangle 7=square^{circ} )

Explanation:

Step1: Find \(m\angle5\)

When two parallel lines are cut by a transversal, \(\angle2\) and \(\angle5\) are alternate interior angles. Alternate interior angles are congruent. So \(m\angle5 = m\angle2\).
Since \(m\angle2 = 103^{\circ}\), then \(m\angle5=103^{\circ}\).

Step2: Find \(m\angle7\)

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are congruent. So \(m\angle7 = m\angle5\).
Because \(m\angle5 = 103^{\circ}\), then \(m\angle7 = 103^{\circ}\).

Answer:

\(m\angle5 = 103^{\circ}\)
\(m\angle7 = 103^{\circ}\)