Answer: VW < VX < WX
========================================================
Step-by-step explanation:
Let's start with the exterior angle 116 degrees.
The interior angle adjacent to this will add to 116 and we'll get 180
(interior angle) + (exterior angle) = 180
(angle VWX) + (angle VWY) = 180
(angle VWX) + (116) = 180
angle VWX = 180 - 116
angle VWX = 64
-----------------
Let's focus solely on the interior angles of triangle VWX
We found angle W to be 64. Angle X is given to be 44. Angle V is unknown, but we can solve for it like such
V+W+X = 180
V+64+44 = 180
V+108 = 180
V = 180-108
V = 72
--------------
The three interior angles of triangle VWX are:
V = 72
W = 64
X = 44
This will determine the order of the side lengths from smallest to largest. Recall that the smallest side of a triangle is always opposite the smallest angle. Similarly, the largest side is always opposite the largest angle.
Based on those V,W,X angle values, we know that
WX = longest side (since the angle opposite V = 72 is largest)
VW = shortest side (since X = 44 is the smallest angle and it is opposite VW)
The order of the sides is therefore:
VW < VX < WX
We don't involve point Y because it's not part of the triangle.
Check out the diagram below for a visual summary.