Subject: Adjacent Angles

Katherine Keys Middle School Teacher

Can a straight angle be an adjacent angle to another angle?

Hi Katherine,

The answer depends on your definitions of both "angle" and "adjacent angles." I would define an angle to be the measure of the rotation about the vertex that brings the first arm of the angle into the second. I would then define two angles to be adjacent if (a) they share the vertex and (b) the second arm of the first angle coincides with the first arm of the second angle. (This simplifies the definition of angle addition.) With this definition the angles could be positive or negative and could measure more than 360 degrees; there would be no restrictions as to what angles could be adjacent.

Euclid did not define "angle measure", and he did not distinguish between positive and negative angles. (Thus an angle of minus 30 degrees would have no meaning to him.) For him the maximum angle was probably the straight angle. Most modern texts allow angles to exceed 180 degrees, so that it would make good sense to have a straight angle adjacent to another angle, as long as they share a vertex and have a common arm that lies between the two outer arms.

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