Question

Question

Use the image to answer the 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 ∠
Remaining Attempts : 3

Answer 1

To determine which angles are complementary, we need to identify pairs of angles that add up to 90 degrees.

From the information given:

• Angle 1 (∠AFB) is a right angle, which means it measures 90 degrees.
• Angles 2 (∠BFC), 3 (∠CFD), 4 (∠DFE), and 5 (∠EFA) need to be evaluated based on their positions and relationships to see if they add up to 90 degrees with angle 1.

When looking closely at the rays:

• Angles 1 and 5, ∠AFB and ∠EFA, are adjacent angles forming a straight line and together they add up to 180 degrees, so they cannot be complementary.
• Angles 2 (∠BFC) and angle 1 (∠AFB) are adjacent, but as mentioned earlier, ∠AFB is right-angled.
• Angles around point F must complete the full angle sums.

If we look at the relationship between angles 2 and 4, we find:

• ∠BFC and ∠DFE are positioned such that along with ∠AFB they complete the straight line from one ray across point F to the other ray.

Thus, the complementary angles in this scenario must be:

• The smaller angle must be ∠BFC (angle 2), and the larger angle is ∠DFE (angle 4).

Therefore, the complementary angles are:

smaller ∠ 2 and larger ∠ 4