Ultimate fate of the universe cosmological constant, which would correspond to a negative energy density and positive pressure, would cause even an open universe to re-collapse to a big crunch. This option has been ruled out by observations. If the average density of the universe exactly equals the critical density so that formula_8, then the geometry of the universe is flat: as in Euclidean geometry, the sum of the angles of a triangle is 180 degrees and parallel lines continuously maintain the same distance. Measurements from Wilkinson Microwave Anisotropy Probe have confirmed the universe is flat with only a 0.4% margin of error. In absence
Internal and external angles simple polygon and a line extended from an adjacent side. The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles. In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180("n"–2"k")° where "n" is the number of vertices and the non-negative number "k" is the number of total revolutions of 360° one undergoes walking around the perimeter of the polygon. In other words, 360"k"° represents the sum of all the exterior angles. For example, for