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: [tex]\angle PQR = 85^{\circ}[/tex]
An intercepted arc measures twice the intercepted angle.
The intercepted angle in the given figure is Arc PQR =[tex]2 \cdot \angle PSR[/tex] ......[1]
First find the [tex]\angle PSR[/tex];
A quadrilateral is cyclic if and only if opposite angles sum to 180°.
then;
[tex]\angle PQR+\angle PSR =180^{\circ}[/tex]
Substitute the value of [tex]\angle PQR = 85^{\circ}[/tex] in above equation we get;
[tex]85^{\circ}+\angle PSR =180^{\circ}[/tex]
Simplify:
[tex]\angle PSR =180^{\circ}-85^{\circ} =95^{\circ}[/tex]
Now; to find the measure of arc PQR ;
[1] ⇒ Arc PQR =[tex]2 \cdot \angle PSR[/tex] = [tex]2 \cdot 95 =190^{\circ}[/tex]
Therefore, the measure of arc PQR is 190 degree.
