Final answer:
We need more information to solve for values of x and a in the geometric problem posed. Typically, setting equations for angles or segment lengths equal allows us to find the unknowns, but the relationships between the angles and segments in this question are not specified.
Step-by-step explanation:
To find the value of x and the measure of angle 1 (m<1>), we need to set up an equation using the information provided:
m<1> = 3x + 12 and m<2> = 2x - 7. If both angles are equal (which is not specified in the question but commonly the case in geometry problems), then we could set the expressions equal to each other to find x.
3x + 12 = 2x - 7
After solving this equation, we'd find the value of x and then substitute it back into the expression for m<1> to find its measure. However, since the relationship between m<1> and m<2> is not stated, we cannot conclusively solve this without additional information.
For RT and WZ, if they are segments of a line and their measures are equal (which is a common assumption), we would set 7a - 2 equal to 4a - 3:
7a - 2 = 4a - 3
By solving for a, we will have the common difference of the segments. Then to find RZ, we would add RT and WZ together:
RZ = RT + WZ
Again, this assumes RT and WZ are connected segments, which is not specified. Therefore, without further context, we cannot provide a conclusive answer.