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

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Question: In a circle, if an 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 circumference?

Options:

  1. 20 degrees
  2. 40 degrees
  3. 80 degrees
  4. 160 degrees

Correct Answer: 40 degrees

Solution: 

The angle subtended at the circumference is half the angle subtended at the center. Therefore, the angle at the circumference is 80/2 = 40 degrees.

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

Practice Questions

Q1
In a circle, if an 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 circumference?
  1. 20 degrees
  2. 40 degrees
  3. 80 degrees
  4. 160 degrees

Questions & Step-by-Step Solutions

In a circle, if an 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 circumference?
  • Step 1: Understand that there is a circle with a center and a circumference.
  • Step 2: Identify that an angle can be formed at the center of the circle by an arc.
  • Step 3: Note that the angle at the center is given as 80 degrees.
  • Step 4: Learn 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 the angle at the center: 80 degrees divided by 2 equals 40 degrees.
  • Step 6: Conclude that the angle subtended by the arc at any point on the circumference is 40 degrees.
  • Angle Subtended by an Arc – The relationship between angles subtended at the center and at the circumference of a circle, where the angle at the circumference is half of that at the center.
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