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

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, -------(1)

And,   -------(2)

According to the question,,

And,  -------(3)

We have to find out or .

Thus, from equation (1), ⇒

Therefore, From equation (3),

⇒

A cyclic quadrilateral is a quadrilateral inscribed in a circle.

The measure of angle QRO is 67 degrees

The given parameters are:

Start by calculating the value of x, as follows:

------ opposite sides of the quadrilateral

So, we have:

Collect like terms

Divide both sides by 7

Next, we calculate the measure of angle R using:

This gives

Hence, the measure of angle QRO is 67 degrees

Read more about cyclic quadrilaterals at:

link