If the smaller angle of a parallelogram is `30^(@)` , then the measure of the bigger angle is

Options

A. `60^(@)`
B. `150^(@)`
C. `180^(@)`
D. `360^(@)`

Answer

To find the measure of the bigger angle in a parallelogram when the smaller angle is given as \(30^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Parallelogram**:
- In a parallelogram, opposite angles are equal and the sum of adjacent angles is \(180^\circ\).

2. **Identifying the Angles**:
- Let the smaller angle be \(30^\circ\). We can denote the bigger angle as \(x\).

3. **Setting Up the Equation**:
- According to the property of parallelograms, the sum of the smaller angle and the bigger angle is \(180^\circ\):
\[ 30^\circ + x = 180^\circ \]

4. **Solving for \(x\)**:
- To find \(x\), we can rearrange the equation:
\[ x = 180^\circ - 30^\circ \]
- Performing the subtraction:
\[ x = 150^\circ \]

5. **Conclusion**:
- Therefore, the measure of the bigger angle in the parallelogram is \(150^\circ\).

### Final Answer:
The measure of the bigger angle is \(150^\circ\).

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