Solution:

Let's assume that angle B is x degrees.

Given:
Angle A = 2 * Angle B
Angle C = (3/2) * Angle B

To find the angles of triangle ABC, we need to determine the values of angle A, angle B, and angle C.

1. Angle A:
Given that Angle A = 2 * Angle B, substituting the value of Angle B as x, we get:

Angle A = 2 * x

2. Angle C:
Given that Angle C = (3/2) * Angle B, substituting the value of Angle B as x, we get:

Angle C = (3/2) * x

3. Sum of Angles in a Triangle:
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:

Angle A + Angle B + Angle C = 180

Substituting the values of Angle A, Angle B, and Angle C, we get:

2x + x + (3/2)x = 180

Simplifying the equation, we have:

(7/2)x = 180

To solve for x, we can multiply both sides of the equation by 2/7:

x = (2/7) * 180
x = 360/7

Now, we have the value of Angle B:

Angle B = 360/7 degrees

4. Finding the values of Angle A and Angle C:
Substituting the value of Angle B in the equations for Angle A and Angle C, we get:

Angle A = 2 * (360/7)
Angle C = (3/2) * (360/7)

Simplifying these equations, we have:

Angle A = 720/7 degrees
Angle C = 540/7 degrees

Therefore, the angles of triangle ABC are:
Angle A = 720/7 degrees
Angle B = 360/7 degrees
Angle C = 540/7 degrees