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