Question

Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠QRO? (5 points)

Quadrilateral OPQR is inscribed in circle N. Angle O is labeled x plus 17 degrees, angle Q is 6x minus 5 degrees, and angle R i

41
67
113
139

Answer 1

Opposite angles of a cyclic quadrilateral are supplementary, so

$x+17+6x-5=180 \\ \\ 7x+12=180 \\ \\ 7x=168 \\ \\ x=24 \\ \\ \\ \implies \angle QRO=2(24)+19=\boxed{67^{\circ}}$