What is the measure of arc QR?
1 answer:
Answer:
answer is the third choice : 104
Step-by-step explanation:
Inscribed Angle Theorem
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
so the intercepted arc is TWICE the measure of an angle inscribed in a circle
1. A central angle is an angle with endpoints located on a circle's circumference and vertex located at the circle's center. A central angle in a circle determines an arc.
2. An inscribed angle is an angle formed by three points on the circle's circumference.
Angle at the Center Theorem: An inscribed angle is half of the central angle (if they determine the same arc).
In your case angles:
1. ∠QSR is insribed (determines the arc QR);
2. ∠QTR is central (determines the arc QR).
Then by Angle at the Center Theorem, m∠QTR=2m∠QSR=2·52°=104°. Arc QR has the same measure as central angle QSR.
gathmath
http://cms5.revize.com/revize/williamsvilleschools/southhigh/mr_quill/geometry_r/docs/Unit%2013/Unit%2013%20Class%20Notes%20KEY.pdf
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