Join the growing community of curious minds on IDNLearn.com and get the answers you need. Join our knowledgeable community to find the answers you need for any topic or issue.

Can you please solve this answer ...

Can You Please Solve This Answer class=

Sagot :

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°

View image Sqdancefan