Use the image to answer the question.

Question

An illustration shows five points upper A, upper B, upper C, upper D, and upper E. Five rays from a common vertex at upper F connect the five points. The angles between them are labeled. The rays extend beyond the five points with an arrow on one side. The rays upper F upper A, upper F upper B, upper F upper C, upper F upper D, and upper F upper E extend through the points from upper F. The ray upper F upper A extends horizontally to the left of upper F. The ray upper F upper B extends vertically upward from upper F. The ray upper F upper C is inclined upward to the right of upper F. The ray upper F upper D extends horizontally to the right of upper F. The ray upper F upper E extends downward to the left of upper F. Angle upper A upper F upper B is marked with a right angle symbol and labeled 1. Angle upper B upper F upper C is labeled as 2. Angle upper C upper F upper D is labeled 3. Angle upper D upper F upper E is labeled 4. Angle upper E upper F upper A is labeled 5.

What two angles are complementary angles? List the smaller angle value first and the larger angle value second.

(1 point)
smaller ∠__ and larger ∠__

Answer 1

To find the complementary angles, we need to identify pairs of angles that sum to 90 degrees. Based on the description:

• ∠AFB is marked with a right angle symbol, so it measures 90 degrees (angle 1).
• ∠BFC is labeled as 2.
• ∠CFD is labeled as 3.
• ∠DFE is labeled as 4.
• ∠EFA is labeled as 5.

Since ∠AFB is already 90 degrees, we should look for angles that complement each other. The angles adjacent to ∠AFB (angle 1) are ∠BFC (angle 2) and ∠EFA (angle 5).

If we assume the arrangement, angle ∠BFC (angle 2) and angle ∠EFA (angle 5) together with ∠AFB would form a full rotation of 360 degrees:

• If angle 2 + angle 5 = 90 degrees, they would be complementary.

Assuming angle 2 is less than angle 5 based on their described positions:

Let’s denote:

• Smaller angle as ∠BFC (2)
• Larger angle as ∠EFA (5)

Therefore, the answer will be:

smaller ∠2 and larger ∠5