No. A wave oscillates at right angles to its direction of propagation and there are plenty of waves in nature: electromagnetic, sonic, in water etc.
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Sure. The angles between edges in a salt crystal are right angles. And that's extremely precise. If you're willing to be a bit more wishy washy, you could say that trees stand at right angles to the ground. Humans walk at right angles to the ground as well.
4 right angles, no other angles.
It has 6 angles, none of which are right angles.
Yes, the 4 inside angles are right angles
No, the angles aren't right angles.