Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 1 = 121 ^ { circ } ). find ( m angle 6 ) and ( m angle 8 ).

Explanation:

Step1: Find \(m\angle 6\)

Since \(\angle1\) and \(\angle6\) are same - side exterior and interior angles. When two parallel lines are cut by a transversal, same - side exterior and interior angles are supplementary.
So, \(m\angle1 + m\angle6=180^{\circ}\)
Substitute \(m\angle1 = 121^{\circ}\) into the equation: \(121^{\circ}+m\angle6 = 180^{\circ}\)
Then \(m\angle6=180^{\circ}- 121^{\circ}=59^{\circ}\)

Step2: Find \(m\angle8\)

\(\angle8\) and \(\angle6\) are vertical angles. Vertical angles are equal.
Since \(m\angle6 = 59^{\circ}\), then \(m\angle8=m\angle6 = 59^{\circ}\)

Answer:

\(m\angle6 = 59^{\circ}\) and \(m\angle8 = 59^{\circ}\)