Question

two parallel lines are cut by a transversal as shown below. note: the figure is not drawn to scale. suppose ( mangle4 = 105^{circ} ). find ( mangle7 ) and ( mangle8 ). ( mangle7= ) select ( mangle8= ) select

Explanation:

Step1: Find \(m\angle2\)

\(\angle4\) and \(\angle2\) are vertical angles. Vertical angles are equal. So \(m\angle2 = m\angle4=105^{\circ}\)

Step2: Find \(m\angle7\)

\(\angle2\) and \(\angle7\) are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are equal. So \(m\angle7=m\angle2 = 105^{\circ}\)

Step3: Find \(m\angle8\)

\(\angle7\) and \(\angle8\) are supplementary angles (they form a linear pair). So \(m\angle8=180^{\circ}-m\angle7\)
Substitute \(m\angle7 = 105^{\circ}\) into the formula: \(m\angle8=180 - 105=75^{\circ}\)

Answer:

\(m\angle7 = 105\), \(m\angle8 = 75\)