**Solution:**

Let's consider two equal velocities, **v1** and **v2**, with a resultant equal to either of the two velocities.

To find the angle between their directions, we can use the concept of vector addition.

**1. Vector Addition:**

When two vectors are added, the resultant vector is obtained by connecting the initial point of the first vector to the final point of the second vector. This can be represented by the parallelogram law of vector addition or the triangle law of vector addition.

**2. Parallelogram Law of Vector Addition:**

According to the parallelogram law of vector addition, if two vectors are represented by the two adjacent sides of a parallelogram, then the diagonal of the parallelogram represents the resultant vector.

**3. Triangle Law of Vector Addition:**

According to the triangle law of vector addition, if two vectors are represented by two sides of a triangle, then the third side represents the resultant vector.

**4. Applying the Concept:**

In this scenario, we have two equal velocities, v1 and v2, and the resultant is equal to either of the two velocities.

Let's assume the angle between the two velocities is θ.

According to the given condition, we can write the equation:

v1 + v2 = v1 .......(1)

or

v1 + v2 = v2 .......(2)

From equation (1), we can say that the resultant is equal to v1. This implies that v1 and v2 are acting in the same direction.

From equation (2), we can say that the resultant is equal to v2. This implies that v1 and v2 are acting in opposite directions.

**5. Conclusion:**

Since the angle between the two velocities is determined by the direction of their resultant, we can conclude that:

- If the two equal velocities have a resultant equal to either of the two velocities, then the angle between their directions is 0 degrees when they are acting in the same direction.

- If the two equal velocities have a resultant equal to either of the two velocities, then the angle between their directions is 180 degrees when they are acting in opposite directions.