A right triangle is 'guaranteed', per se, to have one 90° angle. The other two must add up to 90°, as all triangles have 180° total. How you find the exact measurements of the other two depends on the information you have available to you (which side lengths, if any, you know, and so on). You can use formulas like the law of sines or the law of cosines to help.
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If a triangle is an isosceles triangle as well as being a right-angled triangle, the size of the two angles (that are not right angles) are 45 degrees.
You cannot. The other angles of a right triangle can have any values between 0 and 90 degrees as long as the two of them sum to 90 degrees.
-- If one of the triangles' angle measures is 90 degrees, than it is a right triangle. -- If two of the triangle's angles add up to 90 degrees, then it's a right triangle. -- If the squares of the lengths of two sides add up to the square of the length of the third side, then it's a right triangle.
A right-angle triangle
No there is not. A right triangle has to have an angle of 90 degrees. An equiangular triangle has 3 equal angles. If a right triangle was equiangular, it would be 90 times 3 equaling 270 degrees. There are only 180 degrees in a triangle.