Final answer:
The map projection that maintains angular relations is best characterized as one that preserves shape; known as a conformal projection, with the Mercator projection being a classic example. Option 1 is the correct answer.
Step-by-step explanation:
A map projection that maintains angular relations — also known as maintaining conformality — is one that preserves angles around all locations.
This allows the representation of shapes to be more accurate over smaller areas, despite causing distortion in scale and area, especially towards the poles on a world map. One of the well-known examples of such map projections is the Mercator projection, which projects the world onto a cylinder resulting in latitude lines that are the same length as the equator.
A conformal map projection does not necessarily preserve true distances, direct routes (except from the center), or areas. Therefore, when considering a map projection that preserves shape, the best characterization of a projection that maintains angular relations is: 1) A map projection that preserves shape.