Question

1. in circle r with ( mangle qts = 37^{circ} ), find the measure of minor arc ( overparen{qs} ). ( moverparen{qs} = square^{circ} )

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. That is, if \(\angle QTS\) is an inscribed angle and \(\overset{\frown}{QS}\) is the intercepted arc, then \(m\angle QTS=\frac{1}{2}m\overset{\frown}{QS}\).

Step2: Solve for \(m\overset{\frown}{QS}\)

Given \(m\angle QTS = 37^{\circ}\), from the formula \(m\overset{\frown}{QS}=2\times m\angle QTS\).
Substitute \(m\angle QTS = 37^{\circ}\) into the formula: \(m\overset{\frown}{QS}=2\times37^{\circ}\).

Answer:

\(74\)