Question

which angles are supplementary to each other?
∠1 and ∠3 ∠4 and ∠1 ∠5 and ∠3 ∠7 and ∠1

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze each pair

• For \(\angle1\) and \(\angle3\): They are vertical angles (\(\angle1=\angle3\)), and their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated here).
• For \(\angle4\) and \(\angle1\): They form a linear - pair. A linear - pair of angles is supplementary. By the definition of a linear - pair (two adjacent angles formed by two intersecting lines), \(\angle4+\angle1 = 180^{\circ}\).
• For \(\angle5\) and \(\angle3\): There is no property (like linear - pair or other angle - sum relationships based on the given figure) that makes \(\angle5+\angle3=180^{\circ}\).
• For \(\angle7\) and \(\angle1\): There is no property (like linear - pair or other angle - sum relationships based on the given figure) that makes \(\angle7+\angle1 = 180^{\circ}\).

Answer:

\(\angle4\) and \(\angle1\)