The measure of angle A is determined as "1" by analyzing the given diagram and relationships among angles. The logical progression unveils the value systematically within the context of angle configurations. Therefore, the answer is 1.
Let us call the triangle on the extreme right triangle X, triangle in the middle triangle Y, and triangle on the extreme left triangle Z.
In the given figure, we can see that triangle X has been labeled with angles 1, 2, and 3.
We can establish a relation between the angles of triangle X and Y as:
The angle 3 from triangle X is vertically opposite with one of the angles of triangle Y as we can see in the figure.
Thus, that missing angle becomes 3 also.
Now we have one angle left to interpret in the triangle Y.
That angle, through the given arrangements of triangle X, logically will be equal to 2.
Now we will establish a relationship between triangles Y and Z.
The angle 2 from triangle Y is vertically opposite with one missing angle from triangle Z. Thus, that missing angle becomes 2 also.
Now, following similar steps from triangle Y, we can say that the final angle, which is, angle A in triangle Z, will be equal to 1.
This logical progression, using the given diagram and angle relationships, elucidates the value of A in terms of the measures of other angles, showcasing a systematic approach to solving geometric problems.
Take a look at the attached image to see the final placements of angles.
Hence, the answer is 1.