Question

A quadrilateral 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°

Answer 1

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°