Question

which angles are supplementary to each other? ∠7 and ∠1 ∠12 and ∠11 ∠10 and ∠12 ∠12 and ∠6

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze each pair

• For \(\angle7\) and \(\angle1\): There is no geometric relationship (like forming a linear - pair) that would make their sum \(180^{\circ}\).
• For \(\angle12\) and \(\angle11\): These are adjacent angles formed by two intersecting lines. They form a linear pair. By the definition of a linear pair, \(\angle11+\angle12 = 180^{\circ}\).
• For \(\angle10\) and \(\angle12\): \(\angle10\) and \(\angle12\) are vertical angles. Vertical angles are equal (\(\angle10=\angle12\)), and their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated by the general intersection of lines in the diagram).
• For \(\angle12\) and \(\angle6\): There is no geometric relationship (like forming a linear - pair) that would make their sum \(180^{\circ}\).

Answer:

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