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Vertical walls are important to ensure that buildings - particularly older ones - stay standing up. And a wall that is vertical is at right angles to the floor. Having said that, my children went to a school where the floorplan of each classroom was hexagonal. Furnishing it was a nightmare but it is an innovative design. An igloo probably has no right angles but most other building do.
Shadow of a building have right angles at the base of the building. Braces of buildings have right angles.
Engineers and architects use angles for designs, roads, buildings and sporting facilities. Without angles you wouldn't have the correct height of a ceiling or the correct angel of the roads.
Angles are used in designing and creating structurally sound buildings. It would be pointless if you had a flat roof, wouldn't it?
Some shapes have angles and so they are important in defining the shapes. And angles are absolutely critical for angles. They are the very essence of their existence: if it were not for angles then there would be no angles.