ABCD is a trapezium with ` angleA=90^(@) and AB` parallel to CD. Then ` angleB` is :

Options

A. `90^(@)`
B. `90^(@)-angleC`
C. `360^(@) - angleC`
D. `180^(@) - angleC`

Answer

To solve the problem, we need to find the measure of angle B in trapezium ABCD, where angle A is 90 degrees and AB is parallel to CD.

### Step-by-Step Solution:

1. **Understanding the Trapezium**:
- We have a trapezium ABCD with angle A = 90 degrees and sides AB parallel to CD.

2. **Identifying Angles**:
- Since AB is parallel to CD and angle A is 90 degrees, angle D must also be 90 degrees. This is because the sum of the interior angles on the same side of a transversal (in this case, line AD) is 180 degrees. Therefore, angle D = 90 degrees.

3. **Using the Sum of Angles in a Quadrilateral**:
- The sum of the interior angles of a quadrilateral is 360 degrees. Thus, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360^\circ \]
- Substituting the known values:
\[ 90^\circ + \text{Angle B} + \text{Angle C} + 90^\circ = 360^\circ \]

4. **Simplifying the Equation**:
- Combine the known angles:
\[ 180^\circ + \text{Angle B} + \text{Angle C} = 360^\circ \]
- Now, isolate the sum of angles B and C:
\[ \text{Angle B} + \text{Angle C} = 360^\circ - 180^\circ \]
\[ \text{Angle B} + \text{Angle C} = 180^\circ \]

5. **Finding Angle B**:
- From the equation \(\text{Angle B} + \text{Angle C} = 180^\circ\), we can express angle B in terms of angle C:
\[ \text{Angle B} = 180^\circ - \text{Angle C} \]

6. **Final Answer**:
- Therefore, angle B is given by:
\[ \text{Angle B} = 180^\circ - \text{Angle C} \]

### Conclusion:
The measure of angle B is \(180^\circ - \text{Angle C}\).