Question

Using a straightedge draw a random triangle now carefully cut it out next amputate the angles by snipping through adjacents sides now move the angles together so the vertices all touch

Answer 1

This is usually used as a proof that triangles have 180°.  Look at the attached figures.  If you cut off angle A, angle B and angle C and rotate them so that their vertices touch, you form a half-circle out of them (or a straight line).  We know that half a circle is 1/2 of 360° or 180; therefore all 3 angles in a triangle must add up to 180°.