ABCD is a cyclic trapezium such that AD || BC. If `angle ABC=70^(@)`, then the value of `angleBCD` is :

Options

A. `60^(@)`
B. `70^(@)`
C. `40^(@)`
D. `80^(@)`

Answer

To solve the problem, we need to find the value of angle BCD in the cyclic trapezium ABCD, where AD is parallel to BC and angle ABC is given as 70 degrees.

### Step-by-Step Solution:

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

2. **Label the Angles**:
- Let angle ABC = 70 degrees (given).
- Let angle BCD = x (the angle we need to find).
- Since AD || BC, angle ABC and angle BCD are alternate interior angles.

3. **Use the Property of Cyclic Quadrilaterals**:
- In cyclic quadrilateral ABCD, we have:
\[ \text{Angle A} + \text{Angle C} = 180^\circ \]
\[ \text{Angle B} + \text{Angle D} = 180^\circ \]

4. **Find Angle D**:
- Since angle ABC = 70 degrees, we can find angle D using the property of opposite angles:
\[ \text{Angle B} + \text{Angle D} = 180^\circ \]
\[ 70^\circ + \text{Angle D} = 180^\circ \]
\[ \text{Angle D} = 180^\circ - 70^\circ = 110^\circ \]

5. **Use the Parallel Lines Property**:
- Since AD is parallel to BC, angle D (which is angle ADC) and angle BCD are supplementary:
\[ \text{Angle D} + \text{Angle BCD} = 180^\circ \]
\[ 110^\circ + x = 180^\circ \]
\[ x = 180^\circ - 110^\circ = 70^\circ \]

6. **Conclusion**:
- Therefore, the value of angle BCD is 70 degrees.

### Final Answer:
\[ \text{Angle BCD} = 70^\circ \]