Final answer:
To find the measure of angle STU, subtract the given angles from the sum of the angles in a triangle. Solve for x to substitute it into the equation for m/STU.
Step-by-step explanation:
To find the measure of angle STU, we need to use the fact that the sum of the angles in a triangle is 180 degrees. We are given that m/UST = (25)° and m/TUV = (6x - 9)°. We can subtract those two angles from 180 degrees to find the measure of angle STU. So, we have:
m/STU = 180 - m/UST - m/TUV
m/STU = 180 - (25) - (6x - 9)
m/STU = 180 - 25 - 6x + 9
m/STU = 164 - 6x
We can now substitute the given value of m/STU as (2x 16)° and solve for x:
164 - 6x = 2x + 16
164 = 2x + 16 + 6x
164 = 8x + 16
148 = 8x
x = 18.5
Now that we have the value of x, we can substitute it back into the equation for m/STU:
m/STU = 164 - 6(18.5)
m/STU = 164 - 111
m/STU = 53
Therefore, m/STU is 53 degrees.