An isosceles triangle has no rotational symmetry except for the trivial case of 360 degrees.
Rotational symmetry of 2D shapes
Rotational symmetry is a type of symmetry that occurs when a shape looks the same after it is rotated by a certain angle. The angle of rotation is called the order of rotational symmetry.
For example, an equilateral triangle has rotational symmetry of order 3. This means that it looks the same after it is rotated by 120 degrees, 240 degrees, or 360 degrees.
Rotational symmetry of isosceles triangles
An isosceles triangle has two equal sides and two equal angles. It also has one line of symmetry, which is the line that passes through the midpoint of the base and the apex of the triangle.
However, an isosceles triangle does not have any rotational symmetry, except for the trivial case of 360 degrees. This is because if we rotate an isosceles triangle by any other angle, it will not look the same as it did before.
Visual explanation
The image you provided shows an isosceles triangle with the following rotational symmetries:
Rotational symmetry of 120 degrees about the origin: No
Rotational symmetry of 180 degrees about the origin: Yes
To see why the isosceles triangle does not have rotational symmetry of 120 degrees, imagine rotating the triangle 120 degrees about the origin. The triangle will end up in a different position than it started in.
To see why the isosceles triangle does have rotational symmetry of 180 degrees, imagine rotating the triangle 180 degrees about the origin. The triangle will end up in the same position as it started in.
Conclusion
The only rotational symmetry that applies to the isosceles triangle is rotational symmetry of 180 degrees about the origin.