C = circumference of circle of radius 15 cm. C = 2pi(15)cm = 30pi(cm).

Ratio of arc length to C = 30cm/ (30pi.cm) = (1/pi) = f, say. Central angle subtended by arc = f*(360)deg = (360/pi) deg. = 114.5915590 deg.

:-

C = 2π r

C = 2π x 15 = 30π cm

L arc = 30 cm

30 π cm _________360°

30 cm __________1/π x 360 ° = 114•6 ° (central angle)

Given   r  =  15 cm:

If the central angle is 360°, then the arc length is  2 π r  =  30 π cm

For some central angle  x°, we're given the arc length is 30 cm

So, set up a proportion:

x/360 = 30/(30 π) = 1/π

x = 360 / π

x = 114.6*

30 cm / (2 * pi * 15 cm) * 360 degrees = central angle

2 radians = 114.6 degrees.

Θ = 360*30/(30*PI) = 360/PI °( ≅ 114.59° or 2.00 radians)

30π * x/360= 30

x/360= 1/π

x= 360/π≈ 114.6°