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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 ...
In geometry, a nonagon (/ ˈ n ɒ n ə ɡ ɒ n /) or enneagon (/ ˈ ɛ n i ə ɡ ɒ n /) is a nine-sided polygon or 9-gon.. The name nonagon is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century.
An easy formula for these properties is that in any three points in any shape, there is a triangle formed. Triangle ABC (example) has 3 points, and therefore, three angles; angle A, angle B, and angle C. Angle A, B, and C will always, when put together, will form 360 degrees. So, ∠A + ∠B + ∠C = 360°
One interior angle in a regular triacontagon is 168 degrees, meaning that one exterior angle would be 12°. The triacontagon is the largest regular polygon whose interior angle is the sum of the interior angles of smaller polygons: 168° is the sum of the interior angles of the equilateral triangle (60°) and the regular pentagon (108°).
The sum of the perpendiculars from a regular n-gon's vertices to any line tangent to the circumcircle equals n times the circumradius. [4]: p. 73 The sum of the squared distances from the vertices of a regular n-gon to any point on its circumcircle equals 2nR 2 where R is the circumradius. [4]: p. 73
A regular skew icositetragon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew icositetragon and can be seen in the vertices and side edges of a dodecagonal antiprism with the same D 12d , [2 + ,24] symmetry, order 48.
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°. This argument can be generalized to concave simple ...
The inner angles of the nonagon equal and furthermore = =, = = and = = (see graphic). Applying the cosinus definition in the right angle triangles B F M {\displaystyle \triangle BFM} , B D L {\displaystyle \triangle BDL} and B C J {\displaystyle \triangle BCJ} then yields the proof for Morrie's law: [ 2 ]