The sum of the angles in a triangle add up to 180 degrees.

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Since we know that all the angles in a triangle add up to [color=#0000ff][b]180 degrees[/b][/color], and that we could create [color=#ff00ff][b]3 triangles[/b][/color] inside the pentagon above, the sum of all the angles inside a pentagon can be given by[br][center][math]180^\circ\times3=540^\circ[/math][/center]So the sum of the angles inside a pentagon must be 540 degrees.