Step-by-step Solution:

\[ \text{According to the condition in } \triangle ABC, \quad 2A = 3B = 6C \] \[ \Rightarrow A = 3C, \quad B = 2C \] The sum of the interior angles of a triangle is \(180^\circ\): \[ A + B + C = 180^\circ \] \[ 3C + 2C + C = 180^\circ \] \[ 6C = 180^\circ \] \[ C = 30^\circ \] \[ A = 3C = 3 \times 30^\circ = 90^\circ \] \[ B = 2C = 2 \times 30^\circ = 60^\circ \] Thus, the angles of the triangle are: \[ \boxed{A = 90^\circ, \quad B = 60^\circ, \quad C = 30^\circ} \]