ST bisects angle RSP. m angle RST = (3x+2) and m angle TSP equal 50. Solve for x

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!

Learn how to solve a problem involving angle bisectors and linear equations. Given that ST bisects angle RSP, find the value of x given specific angle measures. Understand the application of the Angle Bisector Theorem in geometry problems. Suitable for high school students.

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