Question

which angles are supplementary to each other?

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle2\) and \(\angle1\)

\(\angle2\) and \(\angle1\) form a linear pair. A linear pair of angles is supplementary. So \(\angle2+\angle1 = 180^{\circ}\).

Step3: Analyze \(\angle8\) and \(\angle1\)

\(\angle8\) and \(\angle1\) are not a linear pair and \(\angle8=\angle2\) (vertically - opposite angles). \(\angle8+\angle1=\angle2 + \angle1=180^{\circ}\)

Step4: Analyze \(\angle3\) and \(\angle7\)

\(\angle3\) and \(\angle7\) are corresponding angles. If the lines are parallel, \(\angle3=\angle7\), but their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated)

Step5: Analyze \(\angle5\) and \(\angle1\)

\(\angle5\) and \(\angle1\) are not a linear pair. \(\angle5=\angle7\) (vertically - opposite angles) and \(\angle7\) and \(\angle1\) are not supplementary (they are alternate interior angles if lines are parallel, but sum is not \(180^{\circ}\))

Answer:

\(\angle8\) and \(\angle1\), \(\angle2\) and \(\angle1\)