Question

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

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

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \(90^{\circ}\). In the diagram, \(\angle 3+\angle 4 = 90^{\circ}\) (since \(\angle ABC = 90^{\circ}\) and \(\angle ABC=\angle 3+\angle 4\)).

Step2: Analyze other options

• For the option “Angle 4 is greater than angle 3” and “Angle 3 is greater than angle 4”: There is no information in the given diagram to compare the measures of \(\angle 3\) and \(\angle 4\) in terms of which one is larger.
• For the option “Angle 3 and 4 are congruent angles”: Congruent angles have equal measures. There is no indication in the diagram that \(\angle 3=\angle 4\).

Answer:

Angles 3 and 4 are complementary angles.