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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 remaining part of the circle? (2023)

Options:

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

Correct Answer: 40 degrees

Exam Year: 2023

Solution: 

The angle subtended at the circumference is half the angle subtended at the center. Therefore, it 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 remaining part of the circle? (2023)
  1. 40 degrees
  2. 80 degrees
  3. 60 degrees
  4. 20 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 remaining part of the circle? (2023)
  • Step 1: Understand that there is a circle with a center point.
  • Step 2: Identify that an angle of 80 degrees is formed at the center of the circle by an arc.
  • Step 3: Recall the rule that states the angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the circumference.
  • Step 4: To find the angle at the circumference, divide the angle at the center (80 degrees) by 2.
  • Step 5: Calculate 80 degrees divided by 2, which equals 40 degrees.
  • Step 6: Conclude that the angle subtended by the same arc at any point on the remaining part of the circle is 40 degrees.
  • Angles in a Circle – The relationship between angles subtended at the center and at the circumference of a circle.
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