Question

list the angle measures of δstu in order from smallest to largest. assume that z is a positive number.

Explanation:

Step1: Match angles to opposite sides

In $\triangle STU$:

• $\angle S$ is opposite $TU = 48z$
• $\angle T$ is opposite $SU = 55z$
• $\angle U$ is opposite $TS = 58z$

Step2: Compare side lengths

Since $z>0$, we have:
$48z < 55z < 58z$

Step3: Relate to angle sizes

In a triangle, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side. So the order of angles from smallest to largest matches the reverse order of their opposite sides.

Answer:

$\angle S < \angle T < \angle U$