absolute measure unit of length The measure unit of angles can be defined geometrically using compass and ruler, but the unit of length can not be defined absolutely so today we have different unit length used (feet, meter miles). Historically different unit length are used. I am interested there are attempts by mathematicians who will define unit of length with mathematical tools by using the achievements of physics or such an attempt would be absurd or meaningless.
 A: Units are by definition relative. There is no absolute, a priori length. In physics, the closest things might be Planck length (and Planck units) the radius of the universe; the Bohr radius of an atom, maybe a Schwarzschild radius?; and the wavelengths of light. But you can't derive them ALL from first principles. There is as of yet no universally defined axiom for any unit of measurement.
Units are interdependent. One needs a system of units. These have cultural origins, but the SI (Système International -- french nomenclature: noun + adjective) system is widely used in science. There are also elementary units. For example, velocity is distance over time, or energy is mass times velocity squared (mass, distance and time are elementary/fundamental quantities). SI addresses this issue from an operational perspective, defining base units and derived units. Then, there is dimensional analysis.
If we take the speed of light in a vacuum as a universal constant (an axiom in special relativity theory), then length units can be derived from time units (or vice versa).
In math, we often use radians for angles, which are related to using the "natural" base $e$ for logarithms, which comes from the area under the curve $y=\frac1x$. There are also solid angles in three dimensions, which are defined as a ratio of volumes. So, some units are a priori or natural. But we also call these unitless numbers (another of which is the fine structure constant).
