in circle t, ∠ptq ≅ ∠rts. what is the measure of $widehat{pq}$? 24° 33° 48° 66°
in circle t, ∠ptq ≅ ∠rts. what is the measure of $widehat{pq}$? 24° 33° 48° 66°
Answer
Explanation:
Step1: Recall the central - angle theorem
In a circle, if two central angles are congruent, then the arcs they intercept are congruent. Since $\angle PTQ\cong\angle RTS$, the arc $\overset{\frown}{PQ}$ and the arc $\overset{\frown}{RS}$ are congruent.
Step2: Find the measure of $\overset{\frown}{RS}$
The measure of an arc is equal to the measure of its central - angle. Given that the measure of $\angle RTS = 66^{\circ}$, the measure of $\overset{\frown}{RS}=66^{\circ}$.
Step3: Determine the measure of $\overset{\frown}{PQ}$
Because $\overset{\frown}{PQ}\cong\overset{\frown}{RS}$, the measure of $\overset{\frown}{PQ}=66^{\circ}$.
Answer:
$66^{\circ}$