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In a circle, if the angle subtended by an arc at the center is 60 degrees, what

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Question: In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the circumference?

Options:

  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 120 degrees

Correct Answer: 30 degrees

Solution: 

The angle subtended at the circumference is half of that at the center, so it is 30 degrees.

In a circle, if the angle subtended by an arc at the center is 60 degrees, what

Practice Questions

Q1
In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the circumference?
  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 120 degrees

Questions & Step-by-Step Solutions

In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the circumference?
  • Step 1: Understand that there is a circle with a center and a circumference.
  • Step 2: Identify that an arc is a part of the circle's circumference.
  • Step 3: Recognize that the angle subtended by the arc at the center of the circle is given as 60 degrees.
  • Step 4: Learn the rule that states the angle subtended at any point on the circumference by the same arc is half of the angle at the center.
  • Step 5: Calculate half of 60 degrees, which is 30 degrees.
  • Step 6: Conclude that the angle subtended at any point on the circumference is 30 degrees.
  • Angle Subtended by an Arc – The relationship between the angle subtended at the center of a circle and the angle subtended at any point on the circumference, specifically that the latter is half of the former.
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