If the measure of WZX is 262, what is the measure of XWY?

Question

anonymous · Answer

@JamesJ

anonymous · Answer

262/2 ? @JamesJ

anonymous · Answer

I got 131

jamesj · Answer

No, that can't be right as the angle is clearly acute, i.e., less than 90 degrees. So what's gone wrong?

anonymous · Answer

Oh wait do you divide by 360 then? @JamesJ

jamesj · Answer

Go back one or two questions when we had the other problem like this. Look very carefully at what arc angle we knew and the angle we were calculating. They corresponded somehow. Does that correspondance apply here? If not, how do you get back to that correspondance.

anonymous · Answer

I think last time we just divided 142 by 2 and got 71..I'm confused on this one @JamesJ

jamesj · Answer

Yes, to apply that formula what arc length do we need? We need the arc length NOT of WZX but of WX.

anonymous · Answer

So how do we find that? @JamesJ

anonymous · Answer

Sorry I'm a bit slow :(

jamesj · Answer

Weeellll ... what's the total angle of a circle?

anonymous · Answer

262! :) @JamesJ

jamesj · Answer

No. 360 degrees.

Hence

WZX + WX = 360

jamesj · Answer

and therefore

WX = 360 - WZX

Make sense?

anonymous · Answer

Ohhhhh so I do 360 - 262? @JamesJ

jamesj · Answer

Yes WX = 360 - 262 = 98

Therefore the angle you are asked for in the question is equal to what?

anonymous · Answer

equal to XWY? @JamesJ

jamesj · Answer

XWY = WX/2

anonymous · Answer

49 @JamesJ

jamesj · Answer

Yes. I'm out of here now.