Question

which angles are supplementary to each other?
∠11 and ∠10 ∠5 and ∠4 ∠8 and ∠3 ∠4 and ∠12

Explanation:

Step1: Recall the definition of supplementary angles

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

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

\(\angle11\) and \(\angle10\) form a linear pair. By the linear - pair postulate, if two angles form a linear pair, then they are supplementary. So \(\angle10+\angle11 = 180^{\circ}\).

Step3: Analyze \(\angle5\) and \(\angle4\)

There is no geometric relationship (such as forming a linear pair or being related through parallel - line properties) that would make \(\angle5+\angle4=180^{\circ}\).

Step4: Analyze \(\angle8\) and \(\angle3\)

There is no geometric relationship (such as forming a linear pair or being related through parallel - line properties) that would make \(\angle8+\angle3 = 180^{\circ}\).

Step5: Analyze \(\angle4\) and \(\angle12\)

There is no geometric relationship (such as forming a linear pair or being related through parallel - line properties) that would make \(\angle4+\angle12=180^{\circ}\).

Answer:

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