In the image provided, we are dealing with points $A'$, $B'$, and $C'$, which are the images of 180-degree rotations of points $A$, $B$, and $C$ around point $O$.

Key Observations:

• The angles provided are:
  • $\angle AOB = 79^\circ$
  • $\angle AOC = 35^\circ$
• Rotating a point by 180 degrees around a center results in its image being directly opposite, with the center being the midpoint of the original point and its image.

To Analyze:

1. Each pair of original points and their images (like $A$ and $A'$) are collinear with point $O$.
2. The points form linear pairs, and each line passes through the origin $O$. Since the rotation is 180 degrees, the angle between any point and its image will always be a straight line (180 degrees).

We can confirm that angles involving any pairs, such as $\angle AOA'$, $\angle BOB'$, and $\angle COC'$, must sum up to 180 degrees.

Would you like me to help calculate additional angles or clarify any specific parts of this setup?

Related Questions:

1. What are the linear relationships between the original points and their images after the rotation?
2. Can we calculate the remaining angles between the lines?
3. How would the diagram change if a different rotation degree, such as 90°, was applied instead?
4. What are the properties of rotations in terms of distances between points and their images?
5. How can this geometric arrangement be used to understand symmetry properties?

Tip: When dealing with 180-degree rotations, every point and its image will be directly opposite each other, forming collinear points with the center of rotation.