Question

PLEASE HELPPPPP !!!!! Question 3(Multiple Choice Worth 5 points) (09.02 MC) Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠QRO? 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 is 2x plus 19 degrees. A) 41 B) 67 C) 113 D) 139

Answer 1

(6x-5)+(x+17)=180
7x+12=180
7x=168
x=24
2x+19=2*24+19=48+19=67
B is the answer. 

Answer 2

Answer: $\angle QRO=67^{\circ}$

Step-by-step explanation:

Since, If a quadrilateral is inscribed in a circle then the sum of one pair of opposite angles must be equal to 180°.

And, here quadrilateral  OPQR is inscribed in circle N.

Thus, $\angle O+\angle Q=180^{\circ}$ -------(1)

And, $\angle P+\angle R=180^{\circ}$   -------(2)

According to the question,$\angle O=(x+17)^{\circ}$, $\angle Q=(6x-5)^{\circ}$

And, $\angle R=(2x+19)^{\circ}$  -------(3)

We have to find out $\angle QRO$ or $\angle R$.

Thus, from equation (1), $(x+17+6x-5)^{\circ}=180^{\circ}$ ⇒$x=24^{\circ}$

Therefore, From equation (3), $\angle QRO=\angle R= (48+19)^{\circ}$

⇒$\angle QRO=67^{\circ}$