Question

line segment ts is tangent to circle o at point n.
if the measure of ∠qnt is 74°, what is the measure of \\(\overarc{qpn}\\)?
148°
74°
37°
212°

Explanation:

Step1: Apply tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc. So, $\angle QNT = \frac{1}{2} \times \text{measure of arc } QPN$.

Step2: Calculate arc QPN

Given $\angle QNT = 74^\circ$, then $\text{measure of arc } QPN = 2 \times 74^\circ = 148^\circ$.

Answer:

148°