ABCD is a cyclic trapezium whose side AD and BC are parallel to each other. If `angle ABC=62^(@)` then the measure of the `angleBCD` is :

Options

A. `120^(@)`
B. `118^(@)`
C. `62^(@)`
D. `28^(@)`

Answer

To solve the problem, we need to find the measure of angle BCD in the cyclic trapezium ABCD, where AD is parallel to BC and angle ABC is given as 62 degrees.

### Step-by-Step Solution:

1. **Understanding the Properties of a Cyclic Trapezium:**
- In a cyclic trapezium, the sum of the opposite angles is 180 degrees.
- Since AD is parallel to BC, we can use the properties of parallel lines and transversals.

2. **Identify the Given Angle:**
- We are given that angle ABC = 62 degrees.

3. **Finding Angle DAB:**
- Since AD is parallel to BC, angle DAB (which is the angle adjacent to angle ABC) can be found using the property of angles on the same side of a transversal.
- Therefore, angle DAB = 180 degrees - angle ABC
- Angle DAB = 180 degrees - 62 degrees = 118 degrees.

4. **Finding Angle BCD:**
- Now, we need to find angle BCD. Since ABCD is a cyclic trapezium, the opposite angles DAB and BCD must also sum to 180 degrees.
- Therefore, angle BCD = 180 degrees - angle DAB
- Angle BCD = 180 degrees - 118 degrees = 62 degrees.

5. **Final Answer:**
- The measure of angle BCD is 62 degrees.

### Summary:
- Angle ABC = 62 degrees
- Angle DAB = 118 degrees
- Angle BCD = 62 degrees