Question

which angles are supplementary to each other?
∠10 and ∠11
∠7 and ∠15
∠5 and ∠16
∠14 and ∠9

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle10\) and \(\angle11\)

\(\angle10\) and \(\angle11\) form a linear pair. By the linear - pair postulate, \(\angle10+\angle11 = 180^{\circ}\).

Step3: Analyze \(\angle7\) and \(\angle15\)

\(\angle7\) and \(\angle15\) are not adjacent and do not form a linear pair. Also, there is no transversal - related property (like same - side interior angles for parallel lines) that would make their sum \(180^{\circ}\).

Step4: Analyze \(\angle5\) and \(\angle16\)

\(\angle5\) and \(\angle16\) are not adjacent and do not form a linear pair. There is no transversal - related property (like same - side interior angles for parallel lines) that would make their sum \(180^{\circ}\).

Step5: Analyze \(\angle14\) and \(\angle9\)

\(\angle14\) and \(\angle9\) are not adjacent and do not form a linear pair. There is no transversal - related property (like same - side interior angles for parallel lines) that would make their sum \(180^{\circ}\).

Answer:

\(\angle10\) and \(\angle11\)