figuring out the sum of angles from the addition of geometrical shapes within a circle

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if you add a number with another you get the sum of the two.(1+1=2, 2+2=4) right? but if you take a circle and put a horizontal line through it you have 4 angles in it. put another circle with a vertical line through it together with the other you should have a total of 8 angles. you actually have a total of twelve angles within your new circle. and if you do this with a triangle you end up with a total of 42 angles. why is this and is there an equasion to figure it out?