Question

in the diagram below, line k is parallel to line m, and line m is parallel to line n. what is the sum of ∠1 and ∠2?

Explanation:

Step1: Use the property of parallel lines (alternate interior angles)

Since \(k\parallel m\), \(\angle1\) and the angle adjacent to \(50^{\circ}\) (on the transversal - line intersecting \(k\) and \(m\)) are alternate - interior angles. Let's call the angle adjacent to \(50^{\circ}\) as \(x\). Then \(x = \angle1\). Also, \(x+50^{\circ}=180^{\circ}\) (linear pair). So, \(\angle1=180^{\circ}- 50^{\circ}=130^{\circ}\).

Step2: Use the property of parallel lines (alternate interior angles)

Since \(m\parallel n\), \(\angle2\) and the angle adjacent to \(150^{\circ}\) (on the transversal - line intersecting \(m\) and \(n\)) are alternate - interior angles. Let's call the angle adjacent to \(150^{\circ}\) as \(y\). Then \(y = \angle2\). Also, \(y + 150^{\circ}=180^{\circ}\) (linear pair). So, \(\angle2=180^{\circ}-150^{\circ}=30^{\circ}\).

Step3: Calculate the sum of \(\angle1\) and \(\angle2\)

\(\angle1+\angle2=(180 - 50)+(180 - 150)\)
\(=130 + 30\)

Answer:

\(160^{\circ}\)