Question

list the angle measures of $\triangle xyz$ in order from smallest to largest, given that $xz = 18s$, $xy = 32s$, and $yz = 19s$. assume that $s$ is a positive number. $m\angle\square < m\angle\square < m\angle\square$

Explanation:

Step1: Relate sides to opposite angles

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

• Side $XZ=18s$ (shortest) $

ightarrow$ opposite $\angle Y$

• Side $YZ=19s$ (middle) $

ightarrow$ opposite $\angle X$

• Side $XY=32s$ (longest) $

ightarrow$ opposite $\angle Z$

Step2: Order angles by side length

Since $18s < 19s < 32s$, the angles opposite these sides follow the same order.

Answer:

$m\angle Y < m\angle X < m\angle Z$