Aquadrilateral pqrs is inscribed in a circle, as shown below: a quadrilateral pqrs is inscribed in a circle. the measure of angle pqr is 75 degrees. what is the measure of arc pqr? (1 point) 210° 255° 105° 75°

Arc PQR measures 210°

An intercepted arc measures twice the intercepted angle. Here, the intercepted angle is ∠PSR. Hence:
Arc PQR = 2 * ∠PSR

1.) Compute for ∠PSR first. Opposite angles in a quadrilateral measures 180°. Hence:
∠PQR + ∠PSR = 180°
     75° + ∠PSR = 180°
               ∠PSR = 180° - 75°
               ∠PSR = 105°

2.) Proceed with computing Arc PQR:
Arc PQR = 2 * ∠PSR
               = 2 * 105°
               = 210°

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