Asked by p

rcle 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 x = m∠RTS. Because Q and S are endpoints of a diameter, TQ is the ray opposite TS, so ∠RTQ = 180° − x. The problem says ∠RTQ is 12° less than ∠RTS, so

180° − x = x − 12° → 2x = 192° → x = 96°.

Thus the central angle RTS measures 96°, so arc RS = 96°. Since P is opposite R and Q is opposite S, the arc QP is the image of arc RS under a half-turn and therefore has the same measure: 96°.

Answer: 96°.