6/1/2023 0 Comments Octagon angle![]() The regular octagon features eight axes of symmetry. The diagonals of an octagon separate its interior into 6 triangles Properties of regular octagons Symmetry ![]() Since the sum of internal angles in one triangle is 180°, it is concluded that 6 triangles, side by side, should measure up to 6x180=1080°. The vertices can be connected in different ways (resulting in different triangles), however the number of triangles remains constantly six. This way, exactly six triangles can be defined inside the octagon. To do so, we have to connect all vertices through straight lines, avoiding any intersections. This can be easily be concluded by finding out how many triangles can be fitted inside the octagon. The sum of the internal angles of any octagon, either convex or concave is always 1080°. Any octagon that is not regular is called irregular. As demonstrated in the figure below, many possible concave octagons can be defined, with equal sides, but unequal interior angles. Having only the sides equal is not adequate, in that matter, since the octagon may be concave, with equal sides. ![]() An octagon is called regular when its sides are equal and also its interior angles are equal. To the contrary, a concave octagon (or polygon) has one or more of its interior angles greater than 180°. A convex octagon has none of its interior angles greater than 180°. An octagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. Octagon is a polygon with eight sides and eight vertices.
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