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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 at any point on the remaining part of the circle?

Options:

  1. 40 degrees
  2. 80 degrees
  3. 100 degrees
  4. 160 degrees

Correct Answer: 40 degrees

Solution: 

The angle subtended at any point on the remaining part of the circle is half of the angle 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 at any point on the remaining part of the circle?
  1. 40 degrees
  2. 80 degrees
  3. 100 degrees
  4. 160 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 at any point on the remaining part of the circle?
  • Step 1: Understand that an arc is a part of the circle's circumference.
  • Step 2: Know that the angle subtended by an arc at the center of the circle is given as 80 degrees.
  • Step 3: Remember the rule that the angle subtended by the same arc at any point on the remaining part of the circle is half of the angle at the center.
  • Step 4: Calculate half of the angle at the center: 80 degrees divided by 2 equals 40 degrees.
  • Step 5: Conclude that the angle subtended at any point on the remaining part of the circle is 40 degrees.
  • Inscribed Angle Theorem – The angle subtended by an arc at any point on the circumference of the circle is half the angle subtended at the center of the circle.
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