Understanding Constructible Angles
To determine which angles can be constructed using a ruler and compass, we need to understand the concept of constructible angles. An angle is constructible if it can be formed using a finite number of steps with these tools.
Key Criteria for Constructibility
- Degree Measurement: An angle is constructible if it can be expressed in degrees that result from repeatedly bisecting angles and using whole number fractions of 360 degrees.
- Constructible Angles: The angles that can be constructed include:
- 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 240°, 270°, 300°, 315°, 330°, and 360°.
- Any angle that can be formed by these through addition or subtraction is also constructible.
Analysis of the Given Angles
- 400°: This angle is not constructible as it exceeds 360°.
- 37.50°: This angle can be expressed as 37.5 = 30 + 7.5. The angle 7.5° can be achieved by bisecting 15° (which is constructible as 30° can be halved).
- 47.50°: This angle cannot be constructed because 47.5° does not correspond to any basic constructible angles or their combinations.
- 350°: Similar to 400°, this angle is not constructible as it is equivalent to -10° in a standard circular measurement.
Conclusion
Among the options, 37.50° is constructible using a ruler and compass because it can be derived from known constructible angles. Therefore, the correct answer is option 'B'.