Question: can the base angle of an isosceles triangle be obtuse

Answer: No, Whether the isosceles triangle is acute, right or obtuse depends on the vertex angle. In Euclidean geometry, the base angles cannot be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle. Since a triangle is obtuse or right if and only if one of its angles is obtuse or right, respectively, an isosceles triangle is obtuse, right or acute if and only if its vertex angle is respectively obtuse, right or acute.