Final answer:
To find the supplementary angle to T, solve for 'x' using the given expressions for vertical angles T and R, then use the value of 'x' to find the measure of angle T, and subtract from 180°.
Step-by-step explanation:
To find the measurement of an angle that is supplementary to angle T, we first need to determine the measure of angle T itself. Since T and R are given as vertical angles, they are equal in measure. Therefore, we can set their measures equal to each other to solve for 'x' and then use that value to find the measure of angle T:
mT = mR
3x + 36 = 6x - 9
To solve for 'x', we collect like terms:
3x - 6x = -9 - 36
-3x = -45
x = 15
Now we find the measure of angle T using the value of 'x':
mT = 3(15) + 36
mT = 45 + 36
mT = 81°
Knowing that supplementary angles add up to 180°, we can find the measure of the angle supplementary to T:
180° - 81° = 99°
Thus, the supplementary angle to T measures 99°.