AC is the diameter of a circumcircle of `DeltaABC`. Chord ED is par allel to the diameter AC. If `/_CBE = 50^@`, then the measure of `/_DEC `is

Options

A. `50^@`
B. `90^@`
C. `60^@`
D. `40^@`

Answer

To solve the problem step by step, we will analyze the given information and apply the relevant geometric principles.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- AC is the diameter of the circumcircle of triangle ABC.
- Chord ED is parallel to the diameter AC.
- Angle CBE = 50°.

2. **Determine Angle ABC**:
- Since AC is the diameter of the circle, angle ABC is an inscribed angle that subtends the diameter. By the property of angles in a semicircle, angle ABC = 90°.

3. **Calculate Angle ABE**:
- We know that angle CBE = 50°.
- Since angle ABC = 90°, we can find angle ABE:
\[ \text{Angle ABE} = \text{Angle ABC} - \text{Angle CBE} = 90° - 50° = 40°. \]

4. **Identify Angle DEC**:
- We need to find angle DEC. Since ED is parallel to AC, we can use the property of alternate interior angles.
- Angle ABE (which we found to be 40°) is equal to angle DEC because they are alternate interior angles formed by the transversal BE intersecting the parallels AC and ED.

5. **Conclusion**:
- Therefore, angle DEC = angle ABE = 40°.

### Final Answer:
\[ \text{Angle DEC} = 40°. \]