Explanation:

- The perimeter of triangle ABC is given as 6 times the arithmetic mean (AM) of the sines of its angles.

- Let’s denote the angles of the triangle ABC by A, B, and C.

- The AM of the sines of angles = (sin A + sin B + sin C) / 3.

- Perimeter = AB + BC + CA = 6 * [(sin A + sin B + sin C) / 3].

- Given BC = v3 and CA = 1.

- Statement 1: ABC is a right-angled triangle.

- If ABC is right-angled, the sides could follow the Pythagorean theorem.

- Calculating for triangle properties can be consistent with right-angle if sides allow sin(90°) scenario.

- Statement 2: The angles of the triangle are in AP.

- The angles in AP hints at potential arithmetic progression, which may include equal angle differences, consistent with certain triangle types.

- Using calculations aligning the properties, it typically verifies:

- Correct Answer: Option 3 - Both 1 and 2.

- Both statements can often be consistent for such a special triangle set-up.

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