Question

list the angle measures of $\triangle uvw$ in order from smallest to largest. assume that $x$ is a positive number.
$m\angle\square < m\angle\square < m\angle\square$

Explanation:

Step1: Link sides to opposite angles

In a triangle, the length of a side is proportional to the measure of its opposite angle.

• Side $4x$ is opposite $\angle W$
• Side $13x$ is opposite $\angle U$
• Side $UV$ (opposite $\angle V$) corresponds to the $97^\circ$ angle

Step2: Compare side lengths

Since $x>0$, $4x < 13x$. The side opposite $\angle V$ is the longest (as $\angle V$ is an obtuse angle, the longest side is always opposite the largest angle in a triangle).

Step3: Match to angle measures

Smallest side ($4x$) → smallest angle ($\angle W$)
Middle side ($13x$) → middle angle ($\angle U$)
Largest side (opposite $\angle V$) → largest angle ($\angle V$)

Answer:

$m\angle W < m\angle U < m\angle V$