The other tutor used trigonometry, but that is not what you
are studying here.  This is geometry, not trigonometry.


The figure is not drawn to scale at all.  We must redraw it more
nearly to scale because it is necssary that YZ which has measure 17 
to be drawn to look longer than WX, which has measure 12.  

Here it is approximately to scale:



Angle W is the largest angle in triangle WXY because it's opposite the
triangle's longest side XY.

Angle XYZ is the largest angle in triangle XYZ because it is opposite the
triangle's longest side.

Therefore the largest of the six angles in both triangles is either
angle W Or angle XYZ.

Since angle WXY = angle XYZ, we can construct a triangle
that's congruent to triangle WXY.

We can locate point P on YZ, such that YP has measure 12, same as WX.
And then draw XP. [This is why we had to redraw the figure because if
you used the drawing at the top you would have to extend YZ.]



Now triangle PYX is congruent to triangle WXY by Side-angle-side.

Therefore the green line XP has the same measure as WY, or 14.



Now we see that Angle XPY is greater than angle XYP because
in triangle XPY, Angle XPY is opposite a side of measure 15
and XYP is opposite a side of measure only 14.

Since Angle XPY has the same measure as angle W, angle W is the
greatest interior angle in either triangle WXY or triangle XYZ.

Edwin