Engage students with the Angle Addition Postulate Scavenger Hunt, a dynamic learning activity designed by All Things Algebra.

Let’s solve the problem shown on card Q in the image.

---

Problem Statement (from Card Q):

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

---

Step-by-Step Solution:

#### Step 1: Understand what a “straight angle” means.
A straight angle measures 180°.

So:
- ∠RST = 180°
- ∠USW = 180°

These are angles formed by straight lines passing through point S.

---

#### Step 2: Use the fact that ray SV bisects ∠RST.

If SV bisects ∠RST, then it splits the 180° angle into two equal parts:

> m∠RSV = m∠VST = 180° ÷ 2 = 90°

So, ∠VST = 90°

---

#### Step 3: Use the given information: m∠WST = 36°

Look at the diagram (or visualize it):

- Point S is the vertex.
- Rays go to R, V, W, T, U.
- ∠WST is the angle between rays SW and ST — given as 36°.
- We just found that ∠VST = 90°.

Notice that ∠VST is made up of ∠VSW + ∠WST.

Wait — let’s be careful with the order of points.

Actually, from the diagram (and standard notation), if we assume rays are arranged around point S in order: R → V → W → T → U (going clockwise or counterclockwise), then:

From ray SV to ray ST is ∠VST = 90°.

Within that, from ray SW to ray ST is ∠WST = 36°.

That means the angle between ray SV and ray SW is:

> ∠VSW = ∠VST - ∠WST = 90° - 36° = 54°

---

#### Step 4: Now find m∠USV.

We know ∠USW is a straight angle = 180°.

∠USW is composed of ∠USV + ∠VSW.

So:

> ∠USV + ∠VSW = 180°

We just found ∠VSW = 54°, so:

> ∠USV = 180° - 54° = 126°

---

✔ Final Answer: m∠USV = 126°

---

🧠 Concept Check:

This problem uses:
- Definition of a straight angle (180°)
- Angle bisector (divides angle into two equal parts)
- Angle addition postulate (if an angle is split into parts, the whole equals the sum of its parts)

---

Let me know if you’d like help with other cards (like A or J) too!