Question

which angles are supplementary to each other?
∠1 and ∠4
∠1 and ∠15
∠12 and ∠2
∠7 and ∠2

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle1\) and \(\angle4\)

\(\angle1\) and \(\angle4\) are vertical angles. Vertical angles are equal (\(\angle1=\angle4\)), and their sum is not \(180^{\circ}\) (unless each is \(90^{\circ}\), which is not indicated here).

Step3: Analyze \(\angle1\) and \(\angle15\)

\(\angle1\) and \(\angle15\) are not adjacent and do not form a linear - pair. Also, there is no transversal - related property (like consecutive interior angles) that would make their sum \(180^{\circ}\).

Step4: Analyze \(\angle12\) and \(\angle2\)

\(\angle12\) and \(\angle2\) are not adjacent and do not form a linear - pair. There is no transversal - related property (such as same - side exterior or interior angles) that would imply their sum is \(180^{\circ}\).

Step5: Analyze \(\angle7\) and \(\angle2\)

\(\angle7\) and \(\angle2\) form a linear - pair. By the definition of a linear - pair of angles (two adjacent angles formed by two intersecting lines), \(\angle7+\angle2 = 180^{\circ}\).

Answer:

\(\angle7\) and \(\angle2\)