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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 remaining part of the circle?

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 remaining part of the circle?
  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 remaining part of the circle?
  • Step 1: Understand that we have a circle with an arc.
  • Step 2: Know that the angle subtended by the arc at the center of the circle is given as 60 degrees.
  • Step 3: Remember the rule that states the angle subtended at the circumference (the edge of the circle) is half of the angle subtended at the center.
  • Step 4: Apply this rule: Half of 60 degrees is 30 degrees.
  • Step 5: Conclude that the angle subtended at any point on the remaining part of the circle is 30 degrees.
  • Inscribed Angle Theorem – The angle subtended at the circumference of a circle is half the angle subtended at the center by the same arc.
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