To find the measures of angles T and S, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
m∠R + m∠S + m∠T = 180°
We know that m∠R = 29°, and we can use the Law of Cosines to find the measure of angle S:
cos(m∠S) = (6^2 + 3^2 - x^2) / (2 * 6 * 3) = 0.9167
m∠S = cos^-1(0.9167) = 23.6°
Now we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle T:
m∠T = 180° - m∠R - m∠S = 180° - 29° - 23.6° = 127.4°
Therefore, m∠T is 127.4° and m∠S is 23.6°.