Question

which angles are supplementary to each other? ∠2 and ∠8 ∠5 and ∠7 ∠8 and ∠6 ∠5 and ∠6

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle5\) and \(\angle6\)

In the given diagram, \(\angle5\) and \(\angle6\) form a linear pair. By the linear - pair postulate, if two angles form a linear pair, then they are supplementary. So \(\angle5+\angle6 = 180^{\circ}\).

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

\(\angle2\) and \(\angle8\) are not adjacent in a way that forms a linear pair. Also, there is no property (like parallel - line properties in this case to make them supplementary directly from the given diagram's basic angle - pair relationships).

Step4: Analyze \(\angle5\) and \(\angle7\)

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are equal (\(\angle5=\angle7\)), and \(\angle5+\angle7
eq180^{\circ}\) (unless \(\angle5 = \angle7=90^{\circ}\), but there is no indication of that from the general diagram).

Step5: Analyze \(\angle8\) and \(\angle6\)

\(\angle8\) and \(\angle6\) are vertical angles. Vertical angles are equal (\(\angle8=\angle6\)), and \(\angle8+\angle6
eq180^{\circ}\) (unless \(\angle8=\angle6 = 90^{\circ}\), but there is no indication of that from the general diagram).

Answer:

\(\angle5\) and \(\angle6\)