Question

Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠QRO?
m∠QPO + (x + 16)° + (6x − 4)° = 360°
m∠QPO = (x + 16)° + (6x − 4)°
m∠QPO + (2x + 16)° = 180°
m∠QPO = (6x − 4)° + (2x + 16)°

Answer 1

@snowflake0531

Answer 2

Do you see how angle QPO makes the arc ORC which is about half the circle

and how angle QRO makes the arc OPC which makes the rest of the circle

so since the entire circle is 360 degrees, that means the arcs both add up to 360

but here we have two inscribed angles (QPO and QRO) and do you remember how

inscribed angle = 1/2 * arc

so that means the two angles have to add up to be HALF of 360

Answer 3

and remember that angle QRO is 2x + 16

Answer 4

@snowflake0531

Answer 5

Well, just do what AZ said
`so that means the two angles have to add up to be HALF of 360`
two angles referring to angle R and angle P
So angle QRO + angle OPQ = 180, since 180 is half of 360
We also have QRO

so, which choice is it

Answer 6

I assume its the only option with 180 degrees in it?

Answer 7

So third

Answer 8

Ye, I think that too

Answer 9

You got it :)