Question

What is the degree of minor arc RS?

30°
45°
60°
90°

Answer 1

60 degrees. Choice #3.

Explanation:

The triangle PST is isosceles, therefore <PST = <STP = 30 degrees. Using the fact that angles in the triangle PST sum up to 180 degrees, we determine the measure of <SPT to be 180-30-30=120 degrees. <SPT is supplementary angle to <SPR, i.e., <SPR = 180 - <SPT = 180-120 = 60 degrees. Therefore the degree of minor arc RS is 60.

Answer 2

TR and QS pass through the P, the center of the circle. Therefore, TR and QS are diameters. That means that both TP and SP are radii, and therefore equal. In other words, triangle TPS is isosceles with TP and SP being its equal sides. The angles opposite TP and SP must therefore be equal.

Angle T = Angle S = 30.

From this, it follows that angle P = 180-(30+30)=120.

The angle supplementary to 120 is 60, which is your answer.