ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If `/_ABC = 72^@`, then the measure of the `/_BCD` is

Options

A. `162^@`
B. `18^@`
C. `108^@`
D. `72^@`

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 72 degrees.

### Step-by-Step Solution:

1. **Understanding the Properties of Cyclic Trapezium**:
- In a cyclic trapezium, the sum of the opposite angles is always 180 degrees. This means that:
\[ \angle ABC + \angle CDA = 180^\circ \]
\[ \angle BCD + \angle ADC = 180^\circ \]

2. **Given Information**:
- We know that \( \angle ABC = 72^\circ \).

3. **Finding Angle CDA**:
- Using the property of cyclic trapezium:
\[ \angle ABC + \angle CDA = 180^\circ \]
- Substituting the known value:
\[ 72^\circ + \angle CDA = 180^\circ \]
- Rearranging to find \( \angle CDA \):
\[ \angle CDA = 180^\circ - 72^\circ = 108^\circ \]

4. **Using Parallel Lines**:
- Since AD is parallel to BC, angles CDA and BCD are corresponding angles. Therefore:
\[ \angle CDA + \angle BCD = 180^\circ \]

5. **Finding Angle BCD**:
- Substituting the value of \( \angle CDA \):
\[ 108^\circ + \angle BCD = 180^\circ \]
- Rearranging to find \( \angle BCD \):
\[ \angle BCD = 180^\circ - 108^\circ = 72^\circ \]

### Final Answer:
The measure of angle BCD is \( 72^\circ \).

---