In circle t, if $\angle \mathrm{PTQ}$ is inscribed and $\angle \mathrm{RTS}$ is a central angle that intercepts the same arc, what is the measure of $\angle \mathrm{PTQ}$ if $\angle \mathrm{RTS}$ measures $66°$?

• A. $48°$
• B. $33°$
• C. $66°$
• D. $24°$

Answer: (B)

Verified step by step guidance

1. Identify the relationship between the inscribed angle \( \angle PTQ \) and the central angle \( \angle RTS \) that intercept the same arc in circle \( t \). Recall that the inscribed angle is always half the measure of the central angle intercepting the same arc.
2. Write the formula expressing this relationship: \( \angle PTQ = \frac{1}{2} \times \angle RTS \).
3. Substitute the given measure of the central angle \( \angle RTS = 66^\circ \) into the formula: \( \angle PTQ = \frac{1}{2} \times 66^\circ \).
4. Simplify the expression to find the measure of the inscribed angle \( \angle PTQ \) in terms of the given central angle.
5. Interpret the result as the measure of \( \angle PTQ \), which is half the measure of \( \angle RTS \), confirming the property of inscribed and central angles intercepting the same arc.