2. (10 points) Among the triangles formed by any 4 points on a plane, the maximum number of obtuse triangles is ( ).
A. 5
B. 2
C. 4
D. 3
【Analysis】According to the problem, among any 4 points on a plane, 3 of them form a needle-angled triangle, and the other 1 point is inside the triangle. When this point is connected to the other 3 points in sequence, it can form 3 obtuse triangles. Based on this, we can find out the maximum number of needle-angled triangles.

【Solution】Solution: As shown in the figure, any 4 points on a plane form 4 obtuse triangles: $\triangle A B C, \triangle A B D, \triangle A C D, \triangle B C D$,

Therefore, among the triangles with any 4 points on a plane as vertices, the maximum number of needle-angled triangles is 4.
Hence, the answer is: $C$.