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