Question

which angles are supplementary to each other?
∠4 and ∠1
∠2 and ∠8
∠4 and ∠2
∠5 and ∠7

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle4\) and \(\angle1\)

\(\angle4\) and \(\angle1\) are adjacent angles forming a linear pair. A linear pair of angles is supplementary. So \(\angle4+\angle1 = 180^{\circ}\).

Step3: Analyze \(\angle2\) and \(\angle8\)

There is no property (like linear - pair, or based on parallel lines and transversals) that would make \(\angle2+\angle8=180^{\circ}\).

Step4: Analyze \(\angle4\) and \(\angle2\)

\(\angle4\) and \(\angle2\) are vertical angles. Vertical angles are equal (\(\angle4=\angle2\)), and their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated here).

Step5: Analyze \(\angle5\) and \(\angle7\)

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are equal (\(\angle5 = \angle7\)), and their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated here).

Answer:

\(\angle4\) and \(\angle1\)