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Is it true that isosceles triangles may be obtuse or acute but never right?
No, it is not true.
Is it true that an isosceles triangle can be acute or obtuse?
Yes, it is true that an isosceles triangle can be acute or obtuse. As long as a triangle has two equal angles and two equal sides, it is isosceles. That situation can occur in both acute (all angles less than 900) and obtuse (one angle more than 900) triangles. Examples are a triangle with the angles being 75-75-30 degrees (acute) and one having angles of 120-30-30 (obtuse). Of course the sides of the angles that are equal would also be equal, so both examples are of isosceles triangles.
Is it true that an obtuse triangle has two obtuse angles and one acute angle?
No
Is it true that an obtuse triangle can have a right angle?
In Euclidean geometry, a triangle must be one of these: acute, obtuse, or right. Maybe there is a non-Euclideangeometry for which some obtuse triangles can contain a right angle, but it doesn't happen in Euclidean geometry.
What is he sum of the angles of an obtuse triangle?
The sum of the interior angles on an Obtuse Triangle is 1800 . This is true of ALL triangles.
