Most of us learn about the functions of lines and angles when we begin learning geometry and algebra. Lines and angles are all around us in everything we see every day. Buildings have lines and angles. Paintings and drawings have lines and angles. Just about anything you can think of has lines and angles. Writing text is done in a line; books are created in square angle format, even parking the car is done in a line, unless you park at an angle.
City and State Design
Look at a map of a city. The majority of streets are laid out in lines. There are times where a curve is involved, usually to move around some type of circular obstacle, then the street reverts back to a line again. When you drive up to a stop sign at a crossroad, you stop then make a right angle turn, a left angle turn, or move straight forward. If you look at a map of the United States, all the states generally have straight lines dividing them from each other. There are occasional irregularities and angles but you don't see states divided into circles. Every state is, basically, divided by a set of lines.
If you look at most of our buildings, they have right angle corners, they are built straight upwards and roofs are either angular or straight across. Even if there is a dome on a church, the principles of lines still applies to the base structure. The base must lay flat and be even on all sides before building the dome. The dome structure must be maintained by measuring each angle and line of point to the center base where all points meet up.
Design and CAD
All designs, whether existing buildings or new products, go through the process of measuring from one point to another so every component fits together properly. If remodeling a kitchen, for example, you must measure the whole kitchen, notate where plumbing is, where electrical outlets are, and where each current cabinet and appliance is located. All measures are to the exact inch. Variations in a wall must be accounted for. All of this is measured in lines, inches or feet, and by degree of angles. If you are building a new engine and have the design in CAD, you also have to explode the diagram to show the inside components and how each piece fits exactly within the engine.
In the Ballet
When you watch a ballet performance, consider that what you see the corps de ballet do is line up exactly and move from one end of the stage to another in unison. Dancers must watch the one in front to stay in the same line when moving together. When dancers make a diagonal line from a back corner to the opposing front corner, they are utilizing angles and lines. The degree that dancers can mimic the ones in front to have exactly the same leg height in arabesque, the same arm lift to the side, the same inclined head on each single dancer, is a sign of an excellent professional corps de ballet. What we learned in geometry works very well on the ballet stage.
If you use a city map and look up a location on the map index, you find the place by using the map's coordinates. If the map has A, B, C, D and so on, running over the top of the map, and 1, 2, 3, 4, and so on, down the side, then you find a place by intersecting at B3, as shown by the map index. Move one finger down the line from the B and one finger across the line from the 3 to find your location. On a world map, follow the intersecting lines of latitude and longitude to find a spot anywhere on the world globe.