Question

list the side lengths of △xyz in order from shortest to longest.

Explanation:

Step1: Find the value of s using angle - sum property

The sum of angles in a triangle is 180°. So, $(s + 52)+7s+8s=180$.
Combining like - terms, we get $16s+52 = 180$.
Subtracting 52 from both sides: $16s=180 - 52=128$.
Dividing both sides by 16, $s = 8$.

Step2: Calculate the angles

Angle $X=s + 52=8 + 52=60^{\circ}$.
Angle $Z = 7s=7\times8 = 56^{\circ}$.
Angle $Y = 8s=8\times8 = 64^{\circ}$.

Step3: Use the angle - side relationship

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest.
The smallest angle is $\angle Z = 56^{\circ}$, the side opposite it is $XY$.
The middle - sized angle is $\angle X = 60^{\circ}$, the side opposite it is $YZ$.
The largest angle is $\angle Y = 64^{\circ}$, the side opposite it is $XZ$.

Answer:

$XY