Question

WZ and XR are diameters. Find the measure of ZWX. Picture below.

Answer 1

First Step: Notice that three angles with vertex C sum to 180 degrees.

112 + m<1 + 63 = 180

Solve for the measure of angle 1 so that you can get the measure of arc XY.

Post what you get, okay.

Then, we can move to the next step. @SouthernBelle730

Answer 2

m<1 = 5? @Directrix

Answer 3

Yes. m<1 = 5 is what I got.

So the measure of arc XY is 5 because the measure of a central angle of a circle is the same as its intercepted arc.

Agree?

(We have more steps to do so don't leave yet.)

Answer 4

Yeah, i'm following you! :)

Answer 5

Then, the measure of arc YZ = 112 because its central angle has measure 112.

And, the measure of arc XZ = 112 + 5 = 117. Check that and let me know if you agree, okay?

Answer 6

Yeah, I agree

Answer 7

Arc XZ = 117.

Arc XZ is the arc cut off by inscribed angle ZWX.

The measure of an inscribed angle of a circle is 1/2 its arc.

So, m<ZWX = 1/2 * 117 = ? @SouthernBelle730

Answer 8

@SouthernBelle730 Post what you get for 1/2 * 117, okay?

Answer 9

58.5?

Answer 10

That is what I got but is it one of the answer options?

Answer 11

It should be.

Answer 12

58.8 is one.

Answer 13

It's close enough though. thank you so much!!

Answer 14

You are welcome.