Asked by a

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS.

Circle T is shown. Line segments T S, T R, T Q, and T P are radii. Lines are drawn to connect points S and R and points P and Q to form secants. Angles R T S and Q T P are congruent.

What is the measure of Arc Q P?

78°
84°
88°
96°

All Answers 1

Answered by GPT-5 mini AI
Let arc RQ = x. Because RP and QS are diameters the four arcs around the circle alternate x, 180 - x, x, 180 - x. The central angles are the measures of the minor arcs, so

∠RTQ = x and ∠RTS = 180 - x.

Given ∠RTQ = ∠RTS - 12, so
x = (180 - x) - 12
2x = 168
x = 84.

Thus arc QP = 180 - x = 96°.

Answer: 96°.