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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.
because it's important to do an 180 turn and math is important
pulleys are important in everyday life because we needed to lift up heay weight objects that a human cant do in their everyday life so pulley is a very important simple machines to humanity.
Do you mean "two-dimensional right angles?" If so, then each side of a cube is a square and so has four right angles.
A hexagon has no right angles what-so-ever.