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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–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Exterior angle – The exterior angle is the supplementary angle to the interior angle. Tracing around a convex n -gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full turn , so the sum of the exterior angles must be 360°.
In Euclidean geometry, the triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate. [1] In the presence of the other axioms of Euclidean geometry, the following statements are equivalent: [2] Triangle postulate: The sum of the angles of a triangle is two ...
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34] The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees, and indeed, this is true for any convex polygon, no matter ...
In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle' [1]) 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.
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This is a special case of the n-gon interior angle sum formula: S = (n − 2) × 180° (here, n=4). [ 2 ] All non-self-crossing quadrilaterals tile the plane , by repeated rotation around the midpoints of their edges.
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