Question

list the angle measures of $\triangle xyz$ in order from smallest to largest. assume that $b$ is a positive number.

$m\angle\square < m\angle\square < m\angle\square$

Explanation:

Step1: Recall triangle side-angle rule

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

Step2: Identify side lengths

Side opposite $\angle X$: $14b$
Side opposite $\angle Z$: $6b$
Side opposite $\angle Y$: $XZ$ (unknown, but $\angle Y=94^\circ$ is obtuse, so it is the largest angle)

Step3: Compare side lengths

Since $b>0$, $6b < 14b$. The side opposite $\angle Y$ is longer than $14b$ (by the law of cosines: $XZ^2=(6b)^2+(14b)^2-2(6b)(14b)\cos94^\circ$, and $\cos94^\circ$ is negative, so $XZ^2 > (6b)^2+(14b)^2$, meaning $XZ>14b$).

Step4: Match angles to side lengths

Shortest side $6b$ → smallest angle $\angle Z$
Middle side $14b$ → middle angle $\angle X$
Longest side $XZ$ → largest angle $\angle Y$

Answer:

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