Question

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

Answer 1

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.