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To determine how many degrees of rotation will result in Triangle XYZ covering Triangle GBM, we need to analyze the geometry of both triangles.

- Triangle XYZ is located in the third quadrant.
- Triangle GBM is located in the first quadrant.

### Step-by-step analysis:

1. **Initial Position**: Triangle XYZ lies in the third quadrant, with vertices close to coordinates \((-2, -2)\), \((-4, -2)\), and \((-4, -4)\).
2. **Target Position**: Triangle GBM is in the first quadrant with its corresponding vertices, seemingly a mirror image of Triangle XYZ.
   
To map Triangle XYZ onto Triangle GBM through rotation, we would need to rotate the figure **180 degrees** about the origin. A 180-degree rotation will flip the triangle from the third quadrant into the first quadrant, allowing it to fully overlap with Triangle GBM.

### Conclusion:
The correct answer is **C. 180 degrees**.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. What happens when you rotate a triangle by 90 degrees around the origin?
2. How can you determine the direction of rotation (clockwise vs. counterclockwise)?
3. What is the difference between reflecting and rotating a geometric figure?
4. How do rotations differ from translations in coordinate geometry?
5. Can a triangle always be mapped onto another triangle using rotation alone?

**Tip**: In geometry, rotating an object 180 degrees around the origin swaps all coordinates \((x, y)\) to \((-x, -y)\).

How many degrees of rotation about the origin will result in Triangle XYZ covering Triangle GBM completely?

Learn how to rotate Triangle XYZ by 180 degrees to completely cover Triangle GBM on a coordinate plane. This geometry problem teaches key concepts about rotations and transformations in Grades 8-10.

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