+4622 In the figure, point \(O\) is the center of the circle, the measure of angle \(RTB\) is 28 degrees, and the measure of angle \(ROB\) is three times the measure of angle \(SOT\). What is the measure of minor arc \(RS\), in degrees?
+129899
Since ROB and SOT are central angles....their measures = the measures of their intercepted arcs
So....We have that
m RTB = (1/2) ( m ROB - m SOT)
28° = (1/2) ( 3m SOT - m SOT) multiply both sides by 2
56° = 2mSOT divide both sides by 2
28° = mSOT
So....mROB = 3 * 28 = 84°
So RS = 180 - 28 - 84 = 68°
