Question

Quadrilateral OPQR is inscribed in Circle N. What is the measure of RQP?

Answer 1

Is this correct?
180 = (2x + 19) + (6x - 5)
180 = 2x + 19 + 6x - 5
8x + 14
166 = 8x
x = 83/4
(2(83/4) + 19)
(41.5 + 19)
180 = 60.5
RQP = 119.5 or 120

Answer 2

@SageWilson @mathstudent55

Answer 3

If a quadrilateral is inscribed in a circle, opposite angles of the quadrilateral are supplementary.

Answer 4

What are your choices

Answer 5

There are no choices

Answer 6

6x - 5 + x + 17 = 180 is the equation I would use.

Answer 7

Thats wrong though. I'm trying to solve for RQP. That equation is for another angle.

Answer 8

Angles R and Q which you used are not known to be supplementary. They are not opposite angles of the quadrilateral.

Answer 9

The marked opposite angles are supplementary. @KatnissEverdeen12

Why is this wrong: 6x - 5 + x + 17 = 180

Answer 10

Since opposite angles of a quadrilateral inscribed in a circle are supplementary, pick two opposite angles that have measures given. There is only one set of opposite angles with measures given. They are angles O and Q.
Add those measures, set the sum equal to 180, and solve for x.
Once you know x, plug in the value of x in the measure of angle Q to find its measure.

Answer 11

@Directrix so should it be
180 = (6x - 5) + (x + 17)?

Answer 12

Let me try to explain to you the thinking behind this problem.

We know that the sum of the measures of the angles of a quadrilateral is 360.
That is not enough to help us here because we don;t know anything about the measure of angle P.

That means we need another piece of information.
We know something about a quadrilateral inscribed in a circle.
In an inscribed quadrilateral, opposite angles are supplementary.

Answer 13

6x - 5 + x + 17 = 180

Solve for x and then use that to find the value of RQP.

@KatnissEverdeen12

Answer 14

okay let me get a notebook

Answer 15

x = 24?

Answer 16

Using what we know about the opposite angles of an inscribed quadrilateral, we now look for a pair of opposite angles that we are given measures (expressions in x).

Angles O and Q have measures given as expressions in x.

Angle O: x + 17
Angle Q: 6x - 5

Add the measures of angles O and Q and set equal to 180:

x + 17 + 6x - 5 = 180

If you solve this equation, you will find the value of x.

Then plug in x into 6x - 5 to find the actual measure of angle Q.

Answer 17

Correct.

Answer 18

Yes.

Then, find 6x - 5 to get the angle measure.

Answer 19

Now plug in 24 into the expression for angle Q to find its measure.

Answer 20

So then i solve this (6(24) - 5)

Answer 21

Yes.

Answer 22

6*24 - 5 =

Answer 23

Yes.

Answer 24

You don't solve. You just evaluate.

Answer 25

Thank you I think I got it from here :) I appreciate your help

Answer 26

You are welcome.

Answer 27

>> (6(24) - 5)

I think this should be 6*24 -5

rather than 6 times the quantity (24 - 5) @KatnissEverdeen12

Answer 28

This is what I did.
6(24) - 5
(144 - 5)
= 139

Answer 29

@Directrix

Answer 30

I have a question if you don't mind

Answer 31

Yes. That is the correct work for 139.

Answer 32

If we are solving for RQP why do we not use R (2x + 19)?

Answer 33

Sorry I'm just new to all of this

Answer 34

Oh wait I understand now. The picture helped

Answer 35

Let me look at the diagram again myself.

Answer 36

Okay

Answer 37

<RQP has vertex at the middle letter: Q.

So, I found < Q and saw that it had measure 6x - 5

Agree?

Answer 38

yes

Answer 39

thank you again. I really appreciate it :)

Answer 40

Then, I remembered a Geometry theorem.

If a quadrilateral is inscribed in a circle, then opposite angles are supplementary.

Answer 41

Opposite <Q is <O.

<O has measure x + 17

That is why this is true: x + 17 + 6x - 5 = 180

Answer 42

thank you :)

Answer 43

The angles you chose when you wrote this: 180 = (2x + 19) + (6x - 5)

are angles R and Q.

They are not opposite angles.

So, the theorem does not apply to them.

Answer 44

Angles R and P are opposite angles and are supplementary.