Does anyone know how to do this geometry problem?

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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

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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

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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.

step-by-step explanation: