Question

An arc on a circle measures

125º. The measure of the central angle, in radians, is within which range?

a) 0 to 2 π radians
b) 0 to π radians
c) π to 2π radians
d) 0 to 2π radians

Answer 1

The measure of the central angle, in radians, is approximately 0.689 radians.

Step-by-step explanation:

The measure of the central angle, in radians, can be found by converting the measure of the arc to radians. Since one complete revolution is equal to 2π radians, we can set up a proportion to find the measure of the central angle.

Let x be the measure of the central angle in radians. We know that 125 degrees is equivalent to π/180 radians. Therefore, we can set up the proportion:

125/360 = x/(2π)

To solve for x, cross multiply and simplify:

360x = 2π * 125

Divide both sides by 360:

x = (2π * 125) / 360

Simplifying further, we get:

x ≈ 0.689 radians