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2006-09-04 01:44 Braindrain0000 223×291× (8937 bytes) Graphic showing vertical angles, where opposite angles have the same measure. Created by me and released into public domain Created by me and released into public domain
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[14] [15] The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical note, [ 15 ] when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to ...
If every internal angle of a simple polygon is less than a straight angle (π radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side. [1]: pp. 261–264
The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.
Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex)
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A transversal produces 8 angles, as shown in the graph at the above left: 4 with each of the two lines, namely α, β, γ and δ and then α 1, β 1, γ 1 and δ 1; and; 4 of which are interior (between the two lines), namely α, β, γ 1 and δ 1 and 4 of which are exterior, namely α 1, β 1, γ and δ.
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