Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle 1 = 51^{circ} ). find ( mangle 6 ) and ( mangle 8 ). ( mangle 6=square^{circ} ) ( mangle 8=square^{circ} )

Explanation:

Step1: Find \(m\angle 6\)

Since \(\angle1\) and \(\angle3\) are vertical angles, \(m\angle3 = m\angle1=51^{\circ}\).
\(\angle3\) and \(\angle6\) are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So \(m\angle6=m\angle3 = 51^{\circ}\).

Step2: Find \(m\angle8\)

\(\angle6\) and \(\angle8\) are vertical angles. Vertical angles are congruent. So \(m\angle8=m\angle6 = 51^{\circ}\).

Answer:

\(m\angle6 = 51^{\circ}\), \(m\angle8 = 51^{\circ}\)