Question

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

Explanation:

Step1: Relate sides to opposite angles

In $\triangle RST$:

• Side $RT=83b$ is opposite $\angle S$
• Side $SR=34b$ is opposite $\angle T$
• Side $ST$ is opposite $\angle R$ (measure $92^\circ$)

Step2: Compare side lengths

Since $b>0$, $34b < 83b$. So the order of sides from shortest to longest is:
$34b < 83b < ST$ (as $\angle R$ is obtuse, its opposite side is the longest)

Step3: Match to opposite angles

In a triangle, shorter sides correspond to smaller opposite angles. So:
$m\angle T < m\angle S < m\angle R$

Answer:

$m\angle T < m\angle S < m\angle R$