What is directed angles?
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Answers
Answer:
di·rect·ed angle. noun. The definition of a directed angle is one that shows a designated direction. An example of a directed angle is one with a counterclockwise arrow going from the base line to the elevated line in the angle showing the direction.
Directed Angles
Directed angles are angles that are directed. There are 2 ways of counting the directed angle \measuredangle ABC:∡ABC:
the angle is positive when the points A, B, CA,B,C are in clockwise order, and negative otherwise, or
the angle is positive when the lines ABAB and BCBC are in counterclockwise order, and negative otherwise.
You should see that both ways are identical to each other. As an example, see the diagram below:
\(\measuredangle ABC= 50^\circ, \measuredangle CBA= -50^\circ\)
\measuredangle ABC= 50^\circ, \measuredangle CBA= -50^\circ∡ABC=50
∘
,∡CBA=−50
∘
We take every angle modulo 180^\circ 180
∘
, i.e.
\cdots=-110^\circ=70^\circ=250^\circ=\cdots.
⋯=−110
∘
=70
∘
=250
∘
=⋯.
This means that in the diagram above, \measuredangle ABC = 50^\circ = 230 ^\circ = -130^\circ = \cdots ∡ABC=50
∘
=230
∘
=−130
∘
=⋯.
Directed angles might seem really annoying and useless at first, but soon you should find it natural and sometimes better than the normal angles.