Question

list the side lengths of δxyz in order from shortest to longest.
z
74w
37w
y
69w
x
□ < □ < □

Explanation:

Step1: Find angle at X

The sum of angles in a triangle is $180^\circ$.
$\angle X = 180 - 74w - 37w = 180 - 111w = 69w$ (matches given value, confirms validity)

Step2: Match sides to opposite angles

In a triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle:

• $\angle Y = 37w$ (smallest angle) → opposite side $XZ$
• $\angle X = 69w$ (middle angle) → opposite side $ZY$
• $\angle Z = 74w$ (largest angle) → opposite side $XY$

Answer:

$XZ < ZY < XY$