Question

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

Explanation:

Step1: Match sides to opposite angles

• Side $10v$ is opposite $\angle R$
• Side $34v$ is opposite $\angle S$
• Side $RS$ is opposite $\angle T$ (given $m\angle T=93^\circ$)

Step2: Compare side lengths

Since $v>0$, $10v < 34v$. By the triangle angle-side relationship, the smaller side corresponds to the smaller opposite angle.

Step3: Identify largest angle

$\angle T$ is $93^\circ$, an obtuse angle, so it is the largest angle in the triangle (the sum of the other two angles is $180^\circ-93^\circ=87^\circ$, so both are acute).

Answer:

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