An angle of a cyclic trapezium is twice the other angle. Find the value of the smaller angle.

Explanation

To solve the problem of finding the smaller angle in a cyclic trapezium where one angle is twice the other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Cyclic Trapezium**:
- A cyclic trapezium is a trapezium (a quadrilateral with one pair of parallel sides) where all vertices lie on a circle.
- In a cyclic trapezium, the sum of the opposite angles is supplementary, meaning they add up to 180 degrees.

2. **Setting Up the Angles**:
- Let the smaller angle be denoted as \( x \).
- According to the problem, the other angle is twice the smaller angle, so we can denote it as \( 2x \).

3. **Using the Property of Supplementary Angles**:
- Since the angles are supplementary, we can write the equation:
\[ x + 2x = 180^\circ \]

4. **Combining Like Terms**:
- Combine the terms on the left side:
\[ 3x = 180^\circ \]

5. **Solving for \( x \)**:
- Divide both sides of the equation by 3 to find the value of \( x \):
\[ x = \frac{180^\circ}{3} = 60^\circ \]

6. **Finding the Other Angle**:
- Now, we can find the value of the other angle \( 2x \):
\[ 2x = 2 \times 60^\circ = 120^\circ \]

7. **Conclusion**:
- The smaller angle \( x \) is \( 60^\circ \).

### Final Answer:
The value of the smaller angle is \( 60^\circ \).