Pentagon Pentagon In geometry, a pentagon (from the Greek πέντε "pente" and γωνία "gonia", meaning "five" and "angle") is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting "regular pentagon" (or "star pentagon") is called a pentagram. A "regular pentagon" has Schläfli symbol {5} and interior angles are 108°. A "regular pentagon" has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its
Sum of angles of a triangle Sum of angles of a triangle In several geometries, a triangle has three "vertices" and three "sides", where three angles of a triangle are formed at each vertex by a pair of adjacent sides. In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °, radians, two right angles, or a half-turn. It was unknown for a long time whether other geometries exist, where this sum is different. The influence of this problem on mathematics was particularly strong during the 19th century. Ultimately, the