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Answer:
∠SPR = 48°
Step-by-step explanation:
The relevant relations are ...
- an inscribed angle is half the measure of the arc it intercepts
- a triangle inscribed in a semicircle is a right triangle
- an exterior angle is equal to the sum of the remote interior angles of a triangle
Since PR is a diameter, triangle PQR is a right triangle with angle PQR being the right angle.
This makes ∠PRQ complementary to ∠RPQ:
∠PRQ = 90° -28° = 62°
Exterior angle RTS is the sum of interior angles TRQ and TQR, so angle TQR can be found to be ...
110° = 62° +∠TQR
∠TQR = 110° -62° = 48° = ∠SQR
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Angle TQR, also angle SQR, subtends arc SR, so is the same measure as angle SPR, which also subtends the same arc.
∠SPR = 48°
