Angles
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A measurement of 2 intersecting lines, based on 360° of a circle.

An angle defines the connection of two vectors (traces), the precursor for all 2D polyhedra.

The smallest form, the triangle, consists of three inside and three central angles. The sum of those all the time equals 180°, half a circle. When all of those angles are equal (60°), the consequence can be an equilateral triangle.

This information permits us to shortly calculate the inside and central angles of the entire set of regular-sided polyhedra. By dividing 360° by the variety of sides we are able to discover the value for the central angle. By subtracting the consequence from 180° we are able to discover the inside angles for that form.

Understanding the connection between the central angle and inside angle of every common polyhedra reveals the fascinating properties of every form.

central angle = 360 ÷ n
inside angle = 180 – (360 ÷ n)
N = Corners
Triangle
Central Angle = 120°
Inside Angle = 60°
Sq.
Central Angle = 90°
Inside Angle = 90°
Pentagon
Central Angle = 72°
Inside Angle = 108°
Hexagon
Central Angle = 60°
Inside Angle = 120°

Discover, that the stability between central and inside angle is unified with the sq. (each are 90°). After that, all subsequent kinds have smaller central angles in comparison with their outer. Within the above desk, solely the Sq. and Triangle are in a position to fill a 2D plain with simply 2 colours. The angles of the Hexagon are inverse to the triangle. The hexagon may tile a 2D area, nonetheless, it requires three colours so as to take action.