Question

which angles are supplementary to each other? ∠9 and ∠3 ∠4 and ∠1 ∠4 and ∠6 ∠12 and ∠10

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze each pair

• For \(\angle9\) and \(\angle3\): They form a linear pair (adjacent angles on a straight - line formed by the intersection of two lines). So, \(\angle9+\angle3 = 180^{\circ}\).
• For \(\angle4\) and \(\angle1\): They are vertical angles (\(\angle4=\angle1\) by the vertical - angles theorem, and \(\angle4+\angle1

eq180^{\circ}\) in general).

• For \(\angle4\) and \(\angle6\): There is no geometric relationship (such as forming a linear pair) that would make their sum \(180^{\circ}\).
• For \(\angle12\) and \(\angle10\): They are vertical angles (\(\angle12 = \angle10\) by the vertical - angles theorem, and \(\angle12+\angle10

eq180^{\circ}\) in general).

Answer:

\(\angle9\) and \(\angle3\)