The measure of the arc RSQ in the circle with an inscribed angle of 24 degrees is 312 degrees.
The relationship between an inscribed angle and the intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the diagram;
Inscribed angle RSQ = 24 degrees
Intercepted arc RQ =?
First, we determine the intercepted arc RQ:
24 = 1/2 × arc RQ
arc RQ = 24 × 2
arc RQ = 48 degrees
Now, to determine the measure of arc RSQ, we subtract arc RQ from 360 degrees.
arc RSQ = 360 - arc RQ
arc RSQ = 360 - 48
arc RSQ = 312°
Therefore, arc RSQ in the circle has a measure of 312 degrees.