The length of an arc is 10cm. find the angle subtending by the arc if the circumference of the circle of which the arc forms part is 60cm.
There are a couple of ways you can do this... you can easily determine the circumference of the circle since you know its radius: C = 2πr. Once you determine this value, you can find out what percentage of the circumference of the circle is covered in 10 cm and multiply that by 360 degrees to get the angle.
The second way is to use the relationship s=rθ, that relates arc length (s) to the circle's radius (r). Since you know s = 10 cm and r = 60 cm, you can solve for theta: θ=s/r = 10 cm/60 cm = 1/6. Note that the angle in this equation is expressed in radians, so if you need to express this in degrees instead, you'll need to apply the conversion that 360 degrees = 2π radians, or that 1 radian is ~57.3 degrees.
The angle ends up being about 9.55 degrees, or 1/6 radians.