Angles Subtended by Arcs An angle subtended by an arc is the angle formed at the endpoint of a ray that sweeps over the arc. The arc itself subtends the...
An angle subtended by an arc is the angle formed at the endpoint of a ray that sweeps over the arc. The arc itself subtends the angle at the center of the circle. We can calculate the angle subtended by an arc by using the angle subtended by a central angle formula.
Formula:
where:
A is the angle subtended by the arc
s is the length of the arc
r is the radius of the circle
Example:
Suppose you have an arc that subtends an angle of 30 degrees at the center of a circle with a radius of 5 cm. Using the formula above, we can calculate the angle subtended by the arc:
Therefore, the angle subtended by the arc is 6 degrees.
Further Notes:
The angle subtended by an arc is always measured in degrees, minutes, and seconds.
An arc subtending an angle of 360 degrees completely subtends the entire circle.
The angle subtended by a complete circle is equal to 360 degrees.
All angles subtended by the same arc are equal to each other