Question

wz and xr are diameters. Find the measure of zwx

Answer 1

The measure of arc ZY is 92 degrees. Okay with that?

Answer 2

yes ..

Answer 3

Okay, now what is the measure of arc XY?

Answer 4

50

Answer 5

XY. 50 is XW.

Answer 6

oh hmm unsure

Answer 7

teacher didnt explain this to well

Answer 8

Alright. Let's look at the angles around the center of the circle. WZ makes a straight angle, which means
angle WCX + angle XCY + angle YCZ = 180

Okay with that?

Answer 9

yes sounds good

Answer 10

Okay. Now we know two of the angles.
angle WCX + angle XCY + angle YCZ = 180
50 + angle XCY + 92 = 180

Good?

Answer 11

okay
i am following so far

Answer 12

Okay. Can you solve for XCY in that equation?

Answer 13

*This equation
50 + angle XCY + 92 = 180

Answer 14

so xyc would be 38 degrees

Answer 15

Yep :)

Answer 16

So if XCY is 38 degrees, what is the measure of arc XY?

Answer 17

it is double right so 72?

Answer 18

No, because XCY is a central angle (meaning that the vertex is the center of the circle).

Answer 19

you lost me sorry

Answer 20

In the first diagram, the angle is a CENTRAL angle, because the vertex is in the center.
In the second diagram, the angle is an INSCRIBED angle, because its vertex is on the outside of the circle.

In the first diagram, the arc measure is EQUAL to the measurement of the central angle
In the second diagram, the arc measure is TWICE the measurement of the inscribed angle

Answer 21

so its 38 degrees

Answer 22

Yes, good. Also 38 degrees.

Answer 23

So what is the measurement of arc XZ?

Answer 24

okay so xz would be 130

Answer 25

Good :)

Answer 26

now do i add the 50 from wx into the equation?

Answer 27

Nah, because it's not part of the angle you're looking for.

Here is what we have. I've taken away all the unimportant parts. Hopefully it will be clear why you don't want arc WX in there:

Answer 28

The angle you're solving for basically comes down to finding x in that drawing.

Answer 29

okay

Answer 30

Ideas on where to go?

Answer 31

this would now be an inscribed angle correct?

Answer 32

Good!

Answer 33

so it would be half of 130?

Answer 34

Yep.

Answer 35

so 65 is angle x

Answer 36

That's right. And you're done.

Answer 37

okay that is not one of my choices for the example though

Answer 38

Hm...it did say angle ZWX, right?

Answer 39

arc i posted the picture above if you need to see it

Answer 40

oh jeez i forgot to put arc in the question

Answer 41

OH. Easy fix though.

Answer 42

okay good

Answer 43

We found the minor arc (the arc that is less than 180 degrees). They wanted the major arc (larger than 180).

How many degrees are in the circle?

Answer 44

360

Answer 45

?

Answer 46

So we want everything EXCEPT what we just found