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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 circumference?

Options:

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

Correct Answer: 40 degrees

Solution: 

Angle at circumference = 1/2 * angle at center = 1/2 * 80 = 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 circumference?
  1. 40 degrees
  2. 80 degrees
  3. 20 degrees
  4. 60 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 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 the rule that the angle subtended at any point on the circumference by the same arc is half of the angle at the center.
  • Step 5: Apply the rule: Take the angle at the center (80 degrees) and divide it by 2.
  • Step 6: Calculate: 80 degrees divided by 2 equals 40 degrees.
  • Step 7: Conclude that the angle subtended at any point on the circumference is 40 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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