Answer: The central angle of the arc is 48 degrees.
Step-by-step explanation: The question has provided the first clue, which is the circumference of the circle, given as 12 units. Also the length of an arc along the same circumference has been given as 8/5 units. The circumference of a circle is calculated as
Circumference = 2Pi x radius
Also the length of an arc is calculated as
Length of an arc = (X/360) x 2Pi x radius (where ‘X’ is the angle subtended by the arc).
Having known the answer to 2Pi x radius which is 12, and the length of the arc which is 8/5, we can now express the length of an arc as
Length of an arc = (X/360) x 2Pi x radius
8/5 = (X/360) x 12
By cross multiplication we now have
(8 x 360)/ (5 x 12) = X
2880/60 = X
48 = X
Therefore the central angle of the arc is 48 degrees.
