Question

Quadrilateral OPQR is inscribed in circle N as shown below. What is the measure of ∠QRO?

a. 40
b. 64
c. 116
d. 140

Answer 1

well u know the sum of any polygon is 360 degrees

Answer 2

btw is angle QPO just x?

Answer 3

if it is then just add all the angles together, set them equal to 360 solve for x, then plug in by into the function representing ∠QRO

Answer 4

Needed Theorem: If a quadrilateral is inscribed in a circle, then opposite angles of the quadrilateral are supplementary.

Angles R and P are supplementary but there is no variable measure given for <P.

So, to get the value of x, solve this equation for x.

m<O + m<Q = 180
x + 16 + 6x - 4 = 180
7x + 12 = 180
@lowcard2 what is the value of x?

Answer 5

24?

Answer 6

Okay.

If x = 24, m<R = 2*24 + 16.
So, m<R = ? @lowcard2

Answer 7

64

Answer 8

Okay.

When you get m<R, recall that <R and <P are supplementary.

So, m<P = 180 - m<R = 180 - 64 = ? @lowcard2

Answer 9

We're not finished.

Answer 10

116

Answer 11

That is what I got.