Given that $ST$ bisects $\angle RSP$, this means that $\angle RST = \angle TSP$. You are given:

$m \angle RST = 3x + 2$ $m \angle TSP = 50^\circ$

Since $ST$ is the bisector, the measures of these angles must be equal:

$3x + 2 = 50$

To solve for $x$, subtract 2 from both sides:

$3x = 48$

Now, divide both sides by 3:

$x = 16$

So, the value of $x$ is 16.

Would you like to explore further details, or do you have any questions?

Here are five related questions to consider:

1. What is the measure of $\angle RST$ after solving for $x$?
2. If $ST$ did not bisect $\angle RSP$, how would the problem change?
3. How do we use the angle bisector theorem in problems involving triangle angles?
4. How would you solve this if given $m \angle RSP$ instead?
5. What would happen if $m \angle TSP$ was given in terms of a different variable?

Tip: Always double-check that all angle relationships given in a problem are correctly used when setting up your equations!