When an angle is bisected at a point, like in your example where the angle is bisected at point \( O \), the original angle is divided into two equal smaller angles. Here’s a more detailed explanation:

### Key Concepts:
- **Angle Bisector**: A line or ray that divides an angle into two equal parts. 
- **Point \( O \)**: This is the point where the bisector intersects the angle. It can either be inside or at the vertex of the angle.

### Understanding Angle Bisectors:
If you have an angle \( \angle ABC \), and a bisector starts from the vertex \( B \) and meets the opposite side at point \( O \), the bisector divides \( \angle ABC \) into two equal angles: 
\[ \angle ABO = \angle OBC \]

### Practical Implications:
- **Symmetry**: The two angles on either side of the bisector are congruent (have the same measure).
- **Proportionality in Geometry**: Angle bisectors often help establish proportional relationships in triangles. For example, if an angle is bisected in a triangle, the opposite sides of those angles are proportional.

Would you like to calculate specific angles or need help with a related geometric problem involving an angle bisector?

### Related Questions:
1. How do you construct an angle bisector using a compass and straightedge?
2. Can angle bisectors be used to find the incenter of a triangle?
3. How does the angle bisector theorem work in triangles?
4. How does an angle bisector affect the lengths of the sides of a triangle?
5. How do you calculate the length of an angle bisector?

**Tip**: In any triangle, the point where all three angle bisectors meet is called the **incenter**, and it is equidistant from all sides of the triangle!

Explore the concept of angle bisectors with a detailed explanation of how an angle is bisected at point O. Learn key geometric principles, including how the angle bisector theorem divides an angle into two equal parts. This content is suitable for students in Grades 7-10.

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