The angles of rotation is 180°.
The image you sent, which shows a triangle ABC rotated about point B to form triangle A'B'C', we can determine the following angles of rotation:
1. 180°
This is the most straightforward answer. When a triangle is rotated 180° about its center, it completely overlaps with its original position. In this case, if we rotate triangle A'B'C' 180° about point B, it will exactly match triangle ABC.
2. 270° clockwise
If we rotate triangle A'B'C' 270° clockwise about point B, it will also overlap with triangle ABC. Imagine rotating a clock hand 270° clockwise – it ends up pointing in the same direction as its starting position, but shifted by three-quarters of a circle. Similarly, rotating triangle A'B'C' 270° clockwise brings it back to the same orientation as triangle ABC, but shifted by three-quarters of a circle.
3. 90° clockwise: This rotation would also map A to A' and C to C', but B would not remain fixed. It would move to B'. This would not bring A'B'C' back to the original position of ABC.