Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 8=99^{circ} ). find ( m angle 1 ) and ( m angle 3 ).

Explanation:

Step1: Find \(m\angle3\)

When two parallel lines are cut by a transversal, \(\angle3\) and \(\angle8\) are vertical angles. Vertical angles are equal. So \(m\angle3 = m\angle8\). Given \(m\angle8 = 99^{\circ}\), then \(m\angle3=99^{\circ}\).

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle3\) are supplementary angles (they form a linear - pair). The sum of the measures of supplementary angles is \(180^{\circ}\). Let \(m\angle1=x\). Then \(x + m\angle3=180^{\circ}\). Substitute \(m\angle3 = 99^{\circ}\) into the equation: \(x+99^{\circ}=180^{\circ}\). Solve for \(x\): \(x=180^{\circ}-99^{\circ}=81^{\circ}\).

Answer:

\(m\angle1 = 81^{\circ}\), \(m\angle3 = 99^{\circ}\)