To find the arclength of a circle that has an angle of 30 degrees to the center of the circle, you need to know two things:
1. The measure of the angle in radians;
2. The radius of the circle.
Since the measure of the angle is given as 30 degrees, and we know that a full circle is 360 degrees, we can write:
Angle in radians = (30 degrees/360 degrees) x 2π radians
Simplifying, we get:
Angle in radians = (1/12) x 2π
Angle in radians = π/6
Now that we know the angle in radians, we can use the formula for the arc length of a circle, which is:
Arc length = angle in radians x radius
Assuming that the radius of the circle is r, we can write:
Arc length = (π/6) x r
Therefore, to find the arc length of the circle, you need to know the radius of the circle, and then multiply it by (π/6).