The correct option is C Any two angles don't share a common side.
A triangle has three sides. So, it has no diagonals.
So, option A can be neglected.
A triangle has three sides. So, any two sides can be considered as adjacent to each other.
So, option B can also be neglected.
A triangle has three sides. So, any two sides meet an one vertex. Hence, any two sides share a common vertex.
So, option D can also be neglected.
Any two angles of a triangle always have a common side.
So, the correct answer is option C.