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In a circle, if the angle subtended by an arc at the center is 80 degrees, what

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Question: In a circle, if the angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle?

Options:

  1. 40 degrees
  2. 80 degrees
  3. 60 degrees
  4. 20 degrees

Correct Answer: 40 degrees

Solution: 

The angle subtended at the circumference is half of that at the center, so it is 80/2 = 40 degrees.

In a circle, if the angle subtended by an arc at the center is 80 degrees, what

Practice Questions

Q1
In a circle, if the angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle?
  1. 40 degrees
  2. 80 degrees
  3. 60 degrees
  4. 20 degrees

Questions & Step-by-Step Solutions

In a circle, if the angle subtended by an arc at the center is 80 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 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 80 degrees.
  • Step 4: Know that the angle subtended by the same arc at any point on the circumference is always half of the angle at the center.
  • Step 5: Calculate half of 80 degrees, which is 80 divided by 2.
  • Step 6: Perform the calculation: 80 / 2 = 40 degrees.
  • Step 7: Conclude that the angle subtended by the arc at any point on the remaining part of the circle is 40 degrees.
  • Inscribed Angle Theorem – The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the circumference.
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