Question

WXYZ is a quadrilateral in which w is 108 degrees x is 88 degrees y is 57 degrees and wxz us 31 degrees calculate wzx and xzy

Answer 1

I know that z is 360 -108 -57-88 but what I don't understand is why wxz is 31 degrees

Answer 2

Does that diagram help a bit?

Answer 3

This is a very interesting puzzle. Thanks for posting it!

- "I don't understand is why wxz is 31 degrees"

Quite simply, it's 31 degrees because they SAID it was 31 degrees.

When I first reconstructed the quad from your description, I drew a zx line and wxz was far less than 31 degrees. Like you, this left me scratching my head.

So then I drew a 31 degree angle and overlaid it on the wx line. That's when I saw the forehead slapper. It turns out that by defining wxz as 31 degrees, you're implicitly defining the length of wz! All I had to do was extend the wz line until z intersected the 31 degree line, and voila!! The quad came together!

Of course, now knowing that wxz is 31 degrees, and w is 108, then wzx is obvious.

Likewise, knowing that wxz is 31 degrees, then zxy must be 88-31. And since y is 57, then xzy is also now obvious.