Ask a New Question
Menu

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 ∠

1 answer

From the description, we can determine the relationships between the angles based on their positioning:

  • Angle \( \angle AFB \) is a right angle (90 degrees).
  • The following angles are labeled:
    • \( \angle BFC = \text{Angle 2} \)
    • \( \angle CFD = \text{Angle 3} \)
    • \( \angle DFE = \text{Angle 4} \)
    • \( \angle EFA = \text{Angle 5} \)

Since in a complete circle, the sum of angles around point F is 360 degrees, we can identify relationships between the labeled angles.

A pair of angles are complementary if they sum up to 90 degrees. Given that \( \angle AFB \) is already 90 degrees, any two other angles that combine with \( \angle AFB \) to make a linear pair with another angle at point F will be complementary.

From the information provided, we can observe the following relationships:

  • The adjacent angle to \( \angle AFB \) is \( \angle EFA \) (angle 5).

Hence, the two angles that are complementary are:

  • \( \angle EFA \) (angle 5)
  • \( \angle AFB \) (angle 1)

Therefore, the smaller angle is \( \angle EFA \) and the larger angle is \( \angle AFB \).

The values would be: smaller ∠ 5 and larger ∠ 1.