SOLUTION: In a regular pentagon, lines are drawn so that every possible pair of vertices are connected. How many triangles are in the resulting figure? choose the answer and explain the r

Question 486604: In a regular pentagon, lines are drawn so that every possible pair of vertices are connected. How many triangles are in the resulting figure?
choose the answer and explain the reason to choose your response
25
35
20
30
In this question, I believe that the answer is either 35 or 30. I am afraid I am counting the same triangles 5 extra times.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

the answer is
The major problem with this is to avoid counting a triangle twice.
Each edge has a small triangle with no cross lines:
Each vertex has a small triange with no cross lines:
Each edge has triangles with cross line (its small triagle merged with one of the small triagles of its 2 vertices):
Each vertex (using its 2 original edges) has a triangle with cross lines:
Each original edge to the opposite vertex has a triangle with little cross lines:

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