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In a circle, if the angle subtended by an arc at the center is 120 degrees, what

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Question: In a circle, if the angle subtended by an arc at the center is 120 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle?

Options:

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

Correct Answer: 60 degrees

Solution: 

The angle subtended at the circumference is half of the angle subtended at the center, so it is 120/2 = 60 degrees.

In a circle, if the angle subtended by an arc at the center is 120 degrees, what

Practice Questions

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

Questions & Step-by-Step Solutions

In a circle, if the angle subtended by an arc at the center is 120 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle?
  • Step 1: Understand that there is a circle with a center and an arc (a part of the circle).
  • Step 2: Know that the angle subtended by the arc at the center of the circle is given as 120 degrees.
  • Step 3: Remember the rule that the angle subtended by the same arc at any point on the circumference (the edge of the circle) is half of the angle at the center.
  • Step 4: Calculate half of the angle at the center: 120 degrees divided by 2 equals 60 degrees.
  • Step 5: Conclude that the angle subtended by the same arc at any point on the remaining part of the circle is 60 degrees.
  • Inscribed Angle Theorem – The angle subtended by an arc at the circumference of a circle is half the angle subtended at the center.
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