A central angle of a circle of radius 30 cm intercepts an arc of 6 cm Express the central angle in radians and in degrees?

A central angle is measured by its intercepted arc.

Let's denote the length of the intercepted arc with s, and the length of the radius r. So,

s = 6 cm and r = 30 cm.

When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian.

To find the angle in our problem we use the following relationship:

measure of an angle in radians = (length of the intercepted arc)/(length of the radius)

measure of our angle = s/r = 6/30 = 1/5 radians.

Now, we need to convert this measure angle in radians to degrees.

Since pi radians = 180 degrees, then

1 radians = 180/pi degrees, so:

1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.