Let's break down the problem step by step:

• Right angle FCD intersects Line AB at point C.
• A ray extends vertically from C to E.
• Angle FCE is congruent to Angle ECD.
• Angle ECD is complementary to Angle DCB.
• Angle ACF is given as 45°.
• Angle FCD is 90°.

We are tasked with analyzing the relationship between Angle DCB and Angle ACF.

Step 1: Analyze Angles Around Point C

• Angle ACF is 45°.
• Since Angle FCE is congruent to Angle ECD, each of these angles must be 45° (because the two angles must sum to 90°, as Angle FCD is a right angle).

Step 2: Complementary Angles

• It is stated that Angle ECD is complementary to Angle DCB. Therefore, the sum of these two angles must be 90°.
  • Since Angle ECD is 45°, Angle DCB must also be 45° to satisfy the complementary condition.

Step 3: Compare Angle DCB and Angle ACF

• Angle DCB is 45° and Angle ACF is also 45°. This means:
  • Angle DCB and Angle ACF are congruent (both equal to 45°).
  • Since their sum is 90°, they are also complementary.

Conclusion:

The correct statement is:

• They are congruent and complementary.

Would you like more details or have any further questions?

Related Questions:

1. What is the sum of complementary angles?
2. How do congruent angles differ from complementary angles?
3. Why is Angle DCB complementary to Angle ECD?
4. Can two angles be congruent and supplementary?
5. What makes an angle a right angle?

Tip: Congruent angles are always equal in measure, while complementary angles sum to 90°.