They don't. If they did then trigonometry would be virtually non-existent.
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Yes. A right triangle is a triangle where one angle is a right angle. If two out of three angles are right angles, then it's an isosceles triangle. If all three angles are right angles, then it is an equilateral triangle.
No.
Yes, an isosceles right triangle will have angles 45-45-90 As a side note, the ratio between the hypotenuse and the sides will always be s: s * √2 where "s" is the length of one of the sides of the isosceles right triangle.
They can but not always.
It is called a 30-60-90 triangle and it is a right triangle whose sides are always in the ratio:1:2:Square root (3).