Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 6 = 77 ^ { circ } ). find ( m angle 1 ) and ( m angle 4 ). ( m angle 1 = ) ( m angle 4 = )

Explanation:

Step1: Find \(m\angle1\)

Since \(\angle6\) and \(\angle2\) are corresponding angles (parallel lines cut by transversal), \(m\angle2 = m\angle6=77^{\circ}\).
\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)).
So, \(m\angle1=180^{\circ}-m\angle2 = 180^{\circ}-77^{\circ}=103^{\circ}\).

Step2: Find \(m\angle4\)

\(\angle4\) and \(\angle2\) are vertical angles.
Vertical angles are equal, so \(m\angle4 = m\angle2=77^{\circ}\).

Answer:

\(m\angle1 = 103^{\circ}\), \(m\angle4 = 77^{\circ}\)