Question

An inscribed angle has a measure of 48°. Determine the measure of the intercepted arc.

Answer 1

I think there's an easier formula but I forgot so let's just conjure our own, eh?
a circle has 360 degrees.
let's say that it's circumference is C
therefore, for a whole circle that's 1 times C.
for half a circle, that's 180/360 times C.
Therefore, for an intercepted arc, it's angle of the inscribed arc/360 times C.
The formula for getting the circumference is diameter times pi

Answer 2

In a circle, a central angle has the same measure as its intercepted arc.
In a circle, an inscribed angle has half the measure of its intercepted arc.

Answer 3

m(arc)AB = a
m<AOB = a
m<ACB = (1/2)a