Final answer:
The value of x is 1.2, RS has a length of 22 units and ST has a length of 10 units. To calculate angle R, additional information is required.
Step-by-step explanation:
The given information suggests that we are dealing with a geometry problem involving line segments. To solve the problem, we need to apply algebraic methods to find the value of x, and then use that value to find the lengths of segments RS and ST.
Solution for (a)
From the given, RS + ST = RT. We know that RS = 22, ST = 5x + 4, and RT = 32. Setting up the equation gives us:
22 + (5x + 4) = 32
Solving for x gives us:
22 + 5x + 4 = 32
5x + 26 = 32
5x = 6
x = 6 / 5
x = 1.2
Solution for (b)
The length of RS is given as 22, which means we don't have to calculate it; it's a part of the given information.
Solution for (c)
Now we need to find the length of ST. Since we found that x = 1.2, we substitute it into the equation ST = 5x + 4:
ST = 5(1.2) + 4
ST = 6 + 4
ST = 10
Solution for (d)
To calculate the measure of angle R, more information is required which is not provided. Typically, the measure of an angle in a line or triangle requires information about the angles or sides of the figure.