Question

which angles are supplementary to each other?
∠12 and ∠7
∠11 and ∠12
∠2 and ∠9
∠10 and ∠4

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). Adjacent supplementary angles form a linear - pair (they share a common side and a common vertex, and their non - common sides form a straight line). Non - adjacent supplementary angles just have the sum of \(180^{\circ}\) without the adjacent requirement.

Step2: Analyze \(\angle11\) and \(\angle12\)

For \(\angle11\) and \(\angle12\), since they are adjacent (share a common side and a common vertex) and their non - common sides form a straight line (they are on a straight line formed by the intersection of two lines). By the definition of a linear pair, if two angles form a linear pair, then they are supplementary. The sum of angles in a linear pair is \(180^{\circ}\).

Step3: Analyze other pairs

• For \(\angle12\) and \(\angle7\): They are not adjacent in a way that their non - common sides form a straight line, and there is no information (like parallel lines and transversals with angle - sum relationships) to suggest their sum is \(180^{\circ}\).
• For \(\angle2\) and \(\angle9\): There is no geometric relationship (such as being on a straight line or having a known angle - sum from parallel lines and transversals) that would make their sum \(180^{\circ}\).
• For \(\angle10\) and \(\angle4\): There is no geometric relationship (such as being on a straight line or having a known angle - sum from parallel lines and transversals) that would make their sum \(180^{\circ}\).

Answer:

\(\angle11\) and \(\angle12\)