In the figure, point A is the center of the circle, the measure of angle RAS is 74 degrees, and the measure of angle RTB is 23 degrees. What is the measure of minor arc BR, in degrees?
+128475 Connect RA and SA
Note that since RA = SA (they are both radii) then triangle RAS is isosceles
So angle SRA = angle TRA= [ 180 - angle RAS ] / 2 = [ 180 -74 ] / 2 = 90 - 37 = 53°
And angle RTB = angle RTA
And considering triangle RAT, by the exterior angle theorem, angle RAB = angle TRA + angle RTA
Angle RAB = 53 + 23 = 76°
But angle RAB is a central angle equaling the measure of minor arc BR = 76°
