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With the help of a ruler and a compass, it is possible to construct an angle of
- a)35°
- b)37.5°
- c)40°
- d)45.7°
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
With the help of a ruler and a compass, it is possible to construct an...
Understanding Constructible Angles
To determine which angles can be constructed using a ruler and compass, we rely on the concept of constructible angles. An angle is constructible if it can be formed using a finite number of steps with these tools.
Criteria for Constructibility
- An angle is constructible if it can be expressed in the form of k * (90°/2^n) where k is an integer and n is a non-negative integer.
- This means the angle must be a rational multiple of 90 degrees.
Evaluating the Given Angles
- 35°: Not constructible since it cannot be expressed in the required form.
- 37.5°:
- This angle can be expressed as 75°/2, which is equal to 90°/2^1.
- Therefore, 37.5° is constructible.
- 40°: Not constructible as it does not fit the criteria.
- 45.7°: Not constructible since it cannot be expressed in the required form.
Conclusion
The only angle from the options given that can be constructed with a ruler and compass is 37.5°. Thus, the correct answer is option B.
To determine which angles can be constructed using a ruler and compass, we rely on the concept of constructible angles. An angle is constructible if it can be formed using a finite number of steps with these tools.
Criteria for Constructibility
- An angle is constructible if it can be expressed in the form of k * (90°/2^n) where k is an integer and n is a non-negative integer.
- This means the angle must be a rational multiple of 90 degrees.
Evaluating the Given Angles
- 35°: Not constructible since it cannot be expressed in the required form.
- 37.5°:
- This angle can be expressed as 75°/2, which is equal to 90°/2^1.
- Therefore, 37.5° is constructible.
- 40°: Not constructible as it does not fit the criteria.
- 45.7°: Not constructible since it cannot be expressed in the required form.
Conclusion
The only angle from the options given that can be constructed with a ruler and compass is 37.5°. Thus, the correct answer is option B.
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Community Answer
With the help of a ruler and a compass, it is possible to construct an...
37.5° (option B) is constructible.
Construct an equilateral triangle to obtain a 60° angle. Bisect the 60° angle to get 30°.
Bisect 30° to obtain 15°, and bisect 15° to obtain 7.5°.
Place the constructed 30° and 7.5° adjacent to each other; their sum is 37.5°. Thus 37.5° can be constructed using ruler and compass.
40° is the central angle of a regular 9-gon (since 360°/9 = 40°); a regular 9-gon is not constructible with ruler and compass, so 40° is not obtainable by classical straightedge-and-compass constructions. The measures 35° and 45.7° are also not obtainable by the simple sequence of standard bisections and sums used above, so they are not constructible here.
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