hiyawesome2005
Answered

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Can you please solve this answer ...

Can You Please Solve This Answer class=

Sagot :

sqdancefan

9514 1404 393

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

__

Angle TQR, also angle SQR, subtends arc SR, so is the same measure as angle SPR, which also subtends the same arc.

  ∠SPR = 48°

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