Question

in circle t, ∠ptq ≅ ∠rts. what is the measure of $widehat{pq}$? 24° 33° 48° 66°

Explanation:

Step1: Recall central - angle arc relationship

In a circle, the measure of an arc is equal to the measure of its central angle. Since \(\angle PTQ\cong\angle RTS\), the measure of arc \(\widehat{PQ}\) is equal to the measure of arc \(\widehat{RS}\).

Step2: Identify the measure of arc \(\widehat{RS}\)

The measure of arc \(\widehat{RS}\) is given by the central - angle that subtends it. Here, the central - angle \(\angle RTS = 66^{\circ}\), so the measure of arc \(\widehat{RS}=66^{\circ}\).

Step3: Determine the measure of arc \(\widehat{PQ}\)

Because \(\angle PTQ\cong\angle RTS\), the measure of arc \(\widehat{PQ}\) is equal to the measure of arc \(\widehat{RS}\). So, the measure of arc \(\widehat{PQ}=66^{\circ}\).

Answer:

\(66^{\circ}\)