Q: Why angle have no dimension?

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The graduation of an angle would usually be expressed in degrees, of which there are 360 for a complete circle.

Height or altitude.

Messier 14 or NGC 6402 has an apparent dimension of 11 minutes of arc.

It is angular displacement which may be measured in radians, or degrees-minutes-seconds. In 3-D it would be stradians

An XY intercept is the point that lays in a two dimensional plane where a line representing an X dimension in that plane and a transverse line at a right angle representing a Y dimension in the same plane intersect.

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The graduation of an angle would usually be expressed in degrees, of which there are 360 for a complete circle.

No, a plane angle does not have a dimension in the sense of length, area, or volume. It is a measurement of rotation or orientation between two intersecting lines in a plane.

Height or altitude.

Use a ruler to make a right angle triangle of dimension 3,4,5 the angle adjacent to the side of 4 units length is 30 degrees.

The analemma would stretch in the north-south dimension.

[ T-1 ] . Reciprocal time, from "degrees per second" .The angle part of it is dimensionless.

Messier 14 or NGC 6402 has an apparent dimension of 11 minutes of arc.

It is angular displacement which may be measured in radians, or degrees-minutes-seconds. In 3-D it would be stradians

isometric drawing create the illusion of 3 dimension by drawing the depth of the object on the both side.. in isometric drawing they are both set on the 30 degree angle..