Question

1. which is an appropriate statement about angles 3 and 4 in the diagram below?

angle 3 and 4 are congruent angles.
angles 3 and 4 are complementary angles.
angle 3 is greater than angle 4.
angle 4 is greater than angle 3.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \(90^{\circ}\). In the diagram, \(\angle3+\angle4 = 90^{\circ}\) (since the two - ray segments form a right - angle at point \(B\)).

Step2: Analyze each option

• Option 1: Congruent angles have equal measures. There is no indication that \(\angle3=\angle4\) from the given diagram.
• Option 2: Since \(\angle3+\angle4 = 90^{\circ}\), by the definition of complementary angles, \(\angle3\) and \(\angle4\) are complementary angles.
• Option 3: There is no information (such as angle measures or proportional markings) to suggest that \(\angle3>\angle4\).
• Option 4: There is no information (such as angle measures or proportional markings) to suggest that \(\angle4>\angle3\).

Answer:

Angles 3 and 4 are complementary angles.