The two sides of the triangle have equal length. The triangle which has equal length on the two side is iscosceles triangle.
The two angles are both acute because they are both 64°. To know whether it's acute or obtuse triangle, we should know the value of third angle. The third angle will define if the status acute/obtuse in triangle.
The sum of angles in triangle is 180°
64° + 64° + the third angle = 180°
128° + the third angle = 180°
the third angle = 180° - 128°
the third angle = 52°
Because all of the angles are acute (below 90°), the triangle on the picture is acute.
The final answer: iscosceles and acute