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]6 triangles[/b][/color] inside the octagon above, then the sum of all the angles inside am octagon is given by[br][br][center][math]180^\circ\times6=1080^\circ[/math][/center]So the sum of the angles inside an octagon must be 1080 degrees.