Answer: Therefore, angle S measures 109 degrees and angle T measures 71 degrees.
Step-by-step explanation: To find the measures of angles S and T, we can use the fact that they form a linear pair, which means they are adjacent and their sum is 180 degrees.
Let's set up an equation using the given information:
m(angle S) + m(angle T) = 180
Substituting the expressions for the measures of the angles:
(5x + 9) + (3x + 11) = 180
Now, let's solve for x:
5x + 9 + 3x + 11 = 180
8x + 20 = 180
8x = 160
x = 20
Now that we have the value of x, we can substitute it back into the expressions for the measures of angles S and T:
m(angle S) = 5x + 9 = 5(20) + 9 = 100 + 9 = 109 degrees
m(angle T) = 3x + 11 = 3(20) + 11 = 60 + 11 = 71 degrees
Therefore, angle S measures 109 degrees and angle T measures 71 degrees.