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?
Practice Questions
1 question
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?
20 degrees
40 degrees
80 degrees
160 degrees
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.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
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.
Steps: 6
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.
