Question

which angles are complementary to each other?

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \(90^{\circ}\).

Step2: Analyze each pair

• For \(\angle1\) and \(\angle5\): There is no indication that \(\angle1+\angle5 = 90^{\circ}\).
• For \(\angle3\) and \(\angle4\): These are adjacent angles formed by intersecting lines. Their sum is \(180^{\circ}-\angle2\) (since \(\angle2 = 90^{\circ}\), \(\angle3+\angle4=90^{\circ}\) is not the case as they are supplementary to \(\angle2\) in a different sense.
• For \(\angle5\) and \(\angle4\): There is no indication that \(\angle5+\angle4 = 90^{\circ}\).
• For \(\angle2\) and \(\angle5\): Since \(\angle1+\angle2+\angle5 = 180^{\circ}\) (a straight - line angle) and \(\angle1 = 90^{\circ}\), then \(\angle2+\angle5=90^{\circ}\)

Answer:

\(\angle2\) and \(\angle5\)