Answer:
Option A is correct.
The measure of Arc PQR is 190 degree
Step-by-step explanation:
Given a cyclic quadrilateral PQRS is inscribed in a circle as shown in figure.
Given:
An intercepted arc measures twice the intercepted angle.
The intercepted angle in the given figure is Arc PQR = ......[1]
First find the ;
A quadrilateral is cyclic if and only if opposite angles sum to 180°.
then;
Substitute the value of in above equation we get;
Simplify:
Now; to find the measure of arc PQR ;
[1] ⇒ Arc PQR = =
Therefore, the measure of arc PQR is 190 degree.