Question

which angles are supplementary to each other?
∠16 and ∠13
∠7 and ∠15
∠6 and ∠2
∠4 and ∠5

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle7\) and \(\angle15\)

\(\angle7\) and \(\angle15\) form a linear - pair. A linear - pair of angles is supplementary (by the linear - pair postulate: if two angles form a linear pair, then they are supplementary).

Step3: Analyze \(\angle16\) and \(\angle13\)

\(\angle16\) and \(\angle13\) are vertical angles. Vertical angles are equal (\(\angle16=\angle13\)), and their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated by the general diagram of intersecting lines).

Step4: Analyze \(\angle6\) and \(\angle2\)

\(\angle6\) and \(\angle2\) are not adjacent in a way that forms a linear pair. Also, there is no information (like parallel lines and transversals with angle - sum properties) to suggest their sum is \(180^{\circ}\).

Step5: Analyze \(\angle4\) and \(\angle5\)

\(\angle4\) and \(\angle5\) are not adjacent in a way that forms a linear pair. And there is no geometric relationship (such as being on a straight line or related through parallel - line angle theorems) to imply their sum is \(180^{\circ}\).

Answer:

\(\angle7\) and \(\angle15\)