MATH SOLVE

4 months ago

Q:
# 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°

Accepted Solution

A:

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°

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°