How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?

25 pairs of vertical angles are formed.

Step-by-step explanation:

Suppose there are N distinct lines, which produces N squared pairs of vertical angles.

If we have 2 distinct lines, then we have 4 pairs of vertical angles are formed.

2 distinct lines, then 2² = 4 pairs of vertical angles

3 distinct lines, then 3² = 9 pairs of vertical angles

4 distinct lines, then 4² = 16 pairs of vertical angles  

Here we have 5 distinct lines, and these lines produces 5² pairs of vertical angles.

So here 25 pairs of vertical angles are formed by 5 distinct lines.

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