Question

which angles are complementary to each other? ∠3 and ∠4 ∠3 and ∠2 ∠5 and ∠4 ∠1 and ∠3

Explanation:

Step1: Recall the definition of complementary angles

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

Step2: Analyze each pair

• For \(\angle3\) and \(\angle4\): They form a linear - pair (sum is \(180^{\circ}\)) as they are adjacent and on a straight line.
• For \(\angle3\) and \(\angle2\): Since \(\angle1 = 90^{\circ}\) (right - angle) and \(\angle1+\angle2+\angle3=180^{\circ}\) (a straight line is \(180^{\circ}\)), then \(\angle2+\angle3=180^{\circ}-\angle1 = 90^{\circ}\).
• For \(\angle5\) and \(\angle4\): They form a linear - pair (sum is \(180^{\circ}\)) as they are adjacent and on a straight line.
• For \(\angle1\) and \(\angle3\): \(\angle1 = 90^{\circ}\), \(\angle1+\angle3>90^{\circ}\)

Answer:

\(\angle3\) and \(\angle2\)