An angle of a quadrilateral is 52° What is the sum of half of its largest angle and twice the smallest angle ?

Options

A. 258°
B. `306^@`
C. 298°
D. Data inadequate

Answer

To solve the problem, we need to analyze the information given about the quadrilateral and the angles involved.

### Step-by-Step Solution:

1. **Understanding the Quadrilateral**:
- A quadrilateral has four angles, and the sum of all angles in a quadrilateral is always 360°.

2. **Given Information**:
- We know one angle of the quadrilateral is 52°. However, we do not have information about the other three angles.

3. **Identifying Largest and Smallest Angles**:
- Since we only know one angle (52°), we cannot definitively determine the largest and smallest angles without additional information about the other angles. The largest angle could be greater than 52°, and the smallest angle could be less than 52° or even equal to it.

4. **Calculating Half of the Largest Angle and Twice the Smallest Angle**:
- Without knowing the values of the other angles, we cannot calculate half of the largest angle or twice the smallest angle.

5. **Conclusion**:
- Since we do not have enough information to determine the largest and smallest angles, we cannot compute the required sum. Therefore, the data provided is inadequate to solve the problem.

### Final Answer:
The data is inadequate to determine the sum of half of the largest angle and twice the smallest angle in the quadrilateral.

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