Since angles T and R are vertical angles, their measures are equal. Therefore, we can set up the equation:
\[ 3x + 36 = 6x - 9 \]
To solve for x, first, rearrange the equation:
\[ 36 + 9 = 6x - 3x \] \[ 45 = 3x \]
Now, divide both sides by 3:
\[ x = 15 \]
Now that we have the value of x, we can find the measure of angle T:
\[ m∠T = 3x + 36 \] \[ m∠T = 3(15) + 36 \] \[ m∠T = 45 + 36 \] \[ m∠T = 81 \]
Thus, the measure of \(\angle T\) is 81.