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 $(-x, -y)$.