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In this problem, we are given the following:

- ∠RST and ∠USW are straight angles (which means each measures 180°).
- Line **SV** bisects ∠RST.
- m∠WST = 36°.
- We are asked to find m∠USV.

### Step-by-Step Solution:

1. **Straight angles:**
   Since ∠RST is a straight angle, we know that:
   \[
   m∠RST = 180°
   \]
   
2. **Understanding the bisector:**
   **SV** bisects ∠RST, meaning that it divides ∠RST into two equal parts. Let m∠RSV be the half of ∠RST:
   \[
   m∠RSV = m∠VST = \frac{180°}{2} = 90°
   \]

3. **Using the given angle:**
   We are told that m∠WST = 36°. Since ∠VST is 90°, we can find m∠WSV:
   \[
   m∠WSV = m∠VST - m∠WST = 90° - 36° = 54°
   \]

4. **Straight angle ∠USW:**
   Since ∠USW is also a straight angle, we know that:
   \[
   m∠USW = 180°
   \]

   Now, m∠USV is part of ∠USW. We can subtract m∠WSV from m∠USW:
   \[
   m∠USV = m∠USW - m∠WSV = 180° - 54° = 126°
   \]

Thus, the measure of m∠USV is **126°**.

---

Would you like further clarification or details on any part of the solution?

### Related Questions:
1. What is the difference between a straight angle and a right angle?
2. How do you calculate the measure of an angle when a line bisects it?
3. If ∠USV were bisected, what would be the measure of each half?
4. Can you explain how to use the angle addition postulate in other problems?
5. What would the measure of m∠WST be if m∠WSV was given as 60°?

### Tip:
When dealing with straight angles, remember that any angles formed along the same line must add up to 180°.

∠RST and ∠USW are straight angles, and SV bisects ∠RST. If m∠WST = 36°, find m∠USV.

Solve for m∠USV when given that ∠RST and ∠USW are straight angles and line SV bisects ∠RST. Detailed solution involves the Angle Addition Postulate and the concept of bisected angles, suitable for Grades 7-10.

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