To find the measure of each interior angle of a regular polygon with "a" sides, we need to use the given information about polygons A and B.

Let's start by finding the number of sides of polygon B in terms of "a". We know that b = 2a, so the number of sides of polygon B is twice the number of sides of polygon A.

Then, let's find the measure of each interior angle of polygon A. We know that the sum of the interior angles of any polygon is given by the formula (n-2) * 180, where n is the number of sides. So, for polygon A, the sum of the interior angles is (a-2) * 180. Since all angles of a regular polygon are equal, each interior angle of polygon A is (a-2) * 180 / a.

Next, let's find the measure of each interior angle of polygon B. We are given that each interior angle of polygon B is 3/2 times each interior angle of polygon A. Therefore, each interior angle of polygon B is (3/2) * [(a-2) * 180 / a].

Now, we can use the information about polygon B to find the number of sides of the final polygon. We know that the measure of each interior angle of a regular polygon is given by the formula (n-2) * 180 / n, where n is the number of sides. So, setting the measure of each interior angle of polygon B equal to the formula, we have:

(3/2) * [(a-2) * 180 / a] = (n-2) * 180 / n.

Simplifying this equation, we get:

3 * (a-2) = 2 * (n-2).

Expanding and simplifying further, we have:

3a - 6 = 2n - 4.

Rearranging the equation, we get:

2n = 3a + 2.

Since n represents the number of sides of the final polygon, we can conclude that the number of sides is a multiple of 2. Therefore, the final polygon is a regular polygon.

Finally, let's find the measure of each interior angle of the final polygon. We know that the measure of each interior angle is given by the formula (n-2) * 180 / n. Substituting the value of n from the equation above, we have:

[(3a + 2) - 2] * 180 / (3a + 2) = 180.

Simplifying the equation, we get:

a = 2.

Therefore, the measure of each interior angle of the final polygon is (2-2) * 180 / 2 = 0 * 180 / 2 = 0 degrees.

However, this result doesn't seem possible since a regular polygon must have non-zero interior angles. Therefore, there might be an error in the given information or calculations.