Sum of angles of a triangle to zero. For a spherical triangle, the sum of the angles is greater than 180° and can be up to 540°. Specifically, the sum of the angles is where "f" is the fraction of the sphere's area which is enclosed by the triangle. Note that spherical geometry does not satisfy several of Euclid's axioms (including the parallel postulate.) Angles between adjacent sides of a triangle are referred to as "interior" angles in Euclidean and other geometries. "Exterior" angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the
The Pentagon was planned accordingly as an irregular pentagon. Concerned that the new building could obstruct the view of Washington, D.C., from Arlington Cemetery, President Roosevelt ended up selecting the Hoover Airport site instead. The building retained its pentagonal layout because a major redesign at that stage would have been costly, and Roosevelt liked the design. Freed of the constraints of the asymmetric Arlington Farms site, it was modified into a regular pentagon which resembled the fortifications of the gunpowder age. On July 28, Congress authorized funding for a new Department of War building in Arlington, which would house the entire department