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

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°.