Final answer:
The measure of the central angle QTS is equal to the measure of the intercepted minor arc QS, which is 120 degrees. If QTS is an inscribed angle, then its measure would be half of the intercepted arc, or 60 degrees.
Step-by-step explanation:
In a circle, the measure of the central angle is equal to the measure of the minor arc it intercepts. In this case, if circle R has a minor arc QS which measures 120 degrees, and points Q, T, and S are on the circle such that QT and TS are radii of the circle, forming a central angle QTS, then by definition, m∠QTS is also 120 degrees.
However, if point T lies on the opposite side of the circle, thus forming the major arc QTS, we need to find the measure of the inscribed angle QTS. The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if the minor arc QS is given as 120 degrees, the measure of the inscribed angle QTS would be 1/2 of 120 degrees, which equals 60 degrees.
To find the measure of angle QTS, we need to use the fact that the measure of an angle formed by a chord and an arc in a circle is half the measure of the intercepted arc. In this case, the intercepted arc QS has a measure of 120 degrees, so the measure of angle QTS is half of that, which is 60 degrees.
It's crucial to know whether point T is inside the circle (forming an inscribed angle) or on the circle (forming a central angle) to determine the correct measure of angle QTS.