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GRE
GRE Quantitative Reasoning Section

Triangles Formed by Pentagon Vertices

Medium Geometry Polygons

Consider a regular pentagon ABCDE. Each interior angle of a regular pentagon can be calculated using the formula:

$$ ext{Interior Angle} = rac{(n - 2) imes 180^ ext{o}}{n} $$

where $$ n $$ is the number of sides of the polygon.

If you were to connect every vertex of the pentagon to every other vertex, how many triangles would be formed with the vertices of the pentagon as the corners of the triangles?

Hint

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