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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

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

From the description:

  • Angle \( \angle AFB \) (1) is a right angle, which is 90 degrees.
  • Angles \( \angle BFC \) (2), \( \angle CFD \) (3), \( \angle DFE \) (4), and \( \angle EFA \) (5) are all the angles around point F.

Since \( \angle AFB \) is already 90 degrees, it cannot be complementary with any other angle.

However, we can analyze the other angles:

  • \( \angle BFC \) + \( \angle CFD \) = \( 2 + 3 \)
  • \( \angle CFD \) + \( \angle DFE \) = \( 3 + 4 \)
  • \( \angle DFE \) + \( \angle EFA \) = \( 4 + 5 \)
  • \( \angle EFA \) + \( \angle AFB \) = \( 5 + 1 \)

To find complementary angles, we will look for pairs that sum to 90 degrees specifically.

Given that:

  • \( \angle BFC \) and \( \angle EFA \) must be complementary:

The smaller angle of these pairs is \( \angle EFA \) (5, if we consider it to be less than \( \angle BFC \)).

Therefore, the two complementary angles can be stated as:

smaller ∠ 5 and larger ∠ 2.