Answer:
Measure of arc PQR is 190°
Step-by-step explanation:
First have a sketch of the quadrilateral PQRS inside a circle
You should notice that the intercepted angle is ∠PSR
You should remember that the intercepted arc PQR is twice the intercepted angle ∠PSR
Find the intercepted angle ∠PSR
Remember that in a quadrilateral opposite angles add up to 180°
Hence;
∠PQR+∠PSR=180°
85 + ∠PSR=180°
∠PSR=180°-85°=95°
Find arc PQR
Arc PQR =2×∠PSR
Arc PQR=2×95°
=190°