The measures of the angles rst are given by the expressions in the table.

To find the value of x, and then find the angles of triangle RST, we first need to set up an equation equal to 180.

First, the equation = 180:

We have 31, x+4, and 3x+9.
What we can do is make an equation in which adds the angles to equal 180.
As so:

31 + x + 4 + 3x + 9 = 180

Combine like terms:

31 + x + 4 + 3x + 9 = 180
44 + x + 3x = 180
44 + 4x = 180

Now, we need to simplify this further by subtracting 44 from each side:

44 - 44 + 4x = 180 - 44
4x = 136

Next, to simplify this equation even further, we need to divide each side by 4 (Resulting in the x being alone on one side of the equation.)

4x / 4 = 136 / 4
x = 136 / 4
x = 34

Awesome! We now know that x = 34!
However, we are not completely finished with this problem. Let's continue.

To find the angles of S and T, we need to substitute 34 in for x:

S:
(x + 4)
(34 + 4)
38 degrees

T:
(3x + 9)
(3(34) + 9)
(102 + 9)
111 degrees

Amazing! We now can conclude all of the angles' measurements:
R = 31
S = 38
T = 111
Also, x = 34.

Hope I could help you out! If my math is wrong or it isn't the answer you were looking for, please let me know!
Have a good one.

The answer is about 23.25 square inches.