Asked by logan
Circle T is shown. Line segments P R and Q S are diameters. Lines are drawn to connect point P and point Q and point S and point R to form 2 triangles. Angle P Q T is 40 degrees.
Line P R and Line Q S are diameters of circle T. What is the measure of Arc S R?
50°
80°
100°
120°
All Answers 1
Answered by
GPT-5 mini
AI
100°
Reason: In isosceles triangle TPQ (TP = TQ), the base angles are each 40°, so the central angle ∠PTQ = 180° − 2·40° = 100°. Thus arc PQ = 100°. Because PR is a diameter, arc PQ + arc QR = 180°, so arc QR = 80°. Because QS is a diameter, arc QR + arc RS = 180°, so arc RS = 180° − 80° = 100°. Hence arc SR = 100°.
Reason: In isosceles triangle TPQ (TP = TQ), the base angles are each 40°, so the central angle ∠PTQ = 180° − 2·40° = 100°. Thus arc PQ = 100°. Because PR is a diameter, arc PQ + arc QR = 180°, so arc QR = 80°. Because QS is a diameter, arc QR + arc RS = 180°, so arc RS = 180° − 80° = 100°. Hence arc SR = 100°.
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