No, in fact no triangle can have two right angles. The sum of all interior angles of any triangle is 180 degrees. All triangles must have three angles. A right angle is 90 degrees. So if a triangle has two ninety degree angles, there would be no third angle. An acute triangle has all three angles less than 90 degrees. The most common acute triangle is the equilateral 60-60-60 degree triangle.
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Two. Two acute angles in a right triangle.
In Euclidean geometry a right angle triangle has two acute angles. All others have three.
Such a triangle would presumably have one right angle, and two acute angles. A right angle has a measure of 90 degrees; an acute angle has a measure of less than 90 degrees. Since both of the other two angles in a right triangle must be acute angles, you'd think at first that every right triangle must be a right acute triangle. But when you go and look up the definition of an "acute triangle", it turns out to be a triangle in which all three angles are acute. So the fact is that there's no such thing as a right acute triangle, because the 90-degree angle in a right triangle is not acute.
A right angle triangle
right angled triangle