Question

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

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 \(\angle4\): There is no information indicating their sum is \(90^{\circ}\).
• For \(\angle3\) and \(\angle1\): There is no information indicating their sum is \(90^{\circ}\).
• For \(\angle5\) and \(\angle3\): There is no information indicating their sum is \(90^{\circ}\).
• For \(\angle2\) and \(\angle1\): Since \(\angle3 = 90^{\circ}\) (right - angle mark), and \(\angle1+\angle2+\angle3 = 180^{\circ}\) (straight - line angle), then \(\angle1+\angle2=180^{\circ}-\angle3 = 90^{\circ}\).

Answer:

\(\angle2\) and \(\angle1\)