Question

which angles are supplementary to each other?
∠11 and ∠4 ∠15 and ∠4 ∠15 and ∠3 ∠11 and ∠12

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze each option

• For \(\angle11\) and \(\angle4\): There is no direct relation (like forming a linear - pair or other angle - sum relations) that would make their sum \(180^{\circ}\).
• For \(\angle15\) and \(\angle4\): There is no direct relation (like forming a linear - pair or other angle - sum relations) that would make their sum \(180^{\circ}\).
• For \(\angle15\) and \(\angle3\):

Since \(\angle15\) and \(\angle3\) form a linear - pair (they are adjacent angles and their non - common sides form a straight line). By the linear - pair postulate, if two angles form a linear - pair, then they are supplementary. So \(\angle15+\angle3 = 180^{\circ}\).

• For \(\angle11\) and \(\angle12\): \(\angle11\) and \(\angle12\) are adjacent angles, but they are vertical angles (not a linear - pair). The sum of vertical angles is not \(180^{\circ}\) (they are equal).

Answer:

\(\angle15\) and \(\angle3\)