Questions: What is m angle QSR? m angle QSR =

Transcript text: What is $m \angle Q S R$ ? \[ m \angle Q S R= \]

Solution

Solution Steps

Step 1: Find the measure of angle RTQ.

Since the measure of angle RTQ is given as 116°, we know that the measure of arc RQ is twice the measure of the inscribed angle RTQ.

m∠RTQ = 116° m(arc RQ) = 2 * m∠RTQ m(arc RQ) = 2 * 116° m(arc RQ) = 232°

Step 2: Find the measure of arc RSQ.

Since RQ is a minor arc and RSQ is a major arc, the sum of the measures of these two arcs is 360°. m(arc RQ) + m(arc RSQ) = 360° 232° + m(arc RSQ) = 360° m(arc RSQ) = 360° - 232° m(arc RSQ) = 128°

Step 3: Find the measure of angle QSR.

The measure of an inscribed angle is half the measure of its intercepted arc. Angle QSR intercepts arc QR. m∠QSR = 1/2 * m(arc QR) m∠QSR = 1/2 * 232° m∠QSR = 116°

However, angle QSR intercepts arc RSQ.
m∠QSR= 1/2 * m(arcRQ) m∠QSR= 1/2 * 128° m∠QSR= 64°

Final Answer

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