Introduction:
When three lines intersect each other, several angles are formed at the points of intersection. These angles can be categorized into different types based on their properties and positions. In this explanation, we will explore the various angles formed by the intersection of three lines.

Types of angles:
1. Vertical angles: When two lines intersect, they form two pairs of vertical angles that are congruent (equal in measure). However, when three lines intersect, multiple pairs of vertical angles are formed.

2. Linear pairs: A linear pair consists of two adjacent angles formed when two lines intersect. When three lines intersect, multiple linear pairs are formed at different points of intersection.

3. Adjacent angles: Adjacent angles are angles that share a common vertex and side but do not overlap. When three lines intersect, numerous pairs of adjacent angles are formed.

4. Alternate interior angles: When a transversal intersects two parallel lines, alternate interior angles are formed. In the case of three intersecting lines, multiple sets of alternate interior angles are created.

5. Corresponding angles: Corresponding angles are formed when a transversal intersects two parallel lines. Similar to alternate interior angles, three intersecting lines create multiple corresponding angles.

6. Supplementary angles: Supplementary angles are pairs of angles that add up to 180 degrees. When three lines intersect, various pairs of supplementary angles are formed.

Conclusion:
In summary, when three lines intersect each other, a multitude of angles are formed at the points of intersection. These angles can be classified into vertical angles, linear pairs, adjacent angles, alternate interior angles, corresponding angles, and supplementary angles. Understanding the properties and relationships of these angles is crucial in geometric analysis and problem-solving.

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