Question

in the figure, two parallel lines, m and l, are cut by a third line, n.

m\angle1 = 74^{circ}

m\angle2 = square^{circ}

m\angle3 = square^{circ}

m\angle4 = square^{circ}

m\angle5 = square^{circ}

m\angle6 = square^{circ}

m\angle7 = square^{circ}

m\angle8 = square^{circ}

Explanation:

Step1: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)).
\(m\angle2=180^{\circ}-m\angle1 = 180 - 74=106^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle1\) and \(\angle3\) are vertical angles (\(\angle1=\angle3\)).
\(m\angle3 = 74^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle2\) and \(\angle4\) are vertical angles (\(\angle2=\angle4\)).
\(m\angle4 = 106^{\circ}\)

Step4: Find \(m\angle5\)

\(\angle1\) and \(\angle5\) are alternate - interior angles (\(\angle1=\angle5\) since \(m\parallel l\)).
\(m\angle5 = 74^{\circ}\)

Step5: Find \(m\angle6\)

\(\angle5\) and \(\angle6\) are supplementary (\(\angle5+\angle6 = 180^{\circ}\)).
\(m\angle6=180 - 74=106^{\circ}\)

Step6: Find \(m\angle7\)

\(\angle5\) and \(\angle7\) are vertical angles (\(\angle5=\angle7\)).
\(m\angle7 = 74^{\circ}\)

Step7: Find \(m\angle8\)

\(\angle6\) and \(\angle8\) are vertical angles (\(\angle6=\angle8\)).
\(m\angle8 = 106^{\circ}\)

Answer:

\(m\angle2 = 106^{\circ}\), \(m\angle3 = 74^{\circ}\), \(m\angle4 = 106^{\circ}\), \(m\angle5 = 74^{\circ}\), \(m\angle6 = 106^{\circ}\), \(m\angle7 = 74^{\circ}\), \(m\angle8 = 106^{\circ}\)