To find the measure of angle S-B-T, we can use the relationship between adjacent angles formed by the lines that intersect at point B.
Given:
- The measure of angle R-B-W = 130 degrees
- The measure of angle T-B-U = 35 degrees
First, we can find the measure of angle S-B-U. Since angles R-B-W and S-B-U are adjacent and form a straight line, their measures must add up to 180 degrees:
\[ \text{Measure of } S-B-U = 180^\circ - \text{Measure of } R-B-W = 180^\circ - 130^\circ = 50^\circ \]
Now, since the line B-T divides angle S-B-U into two angles (S-B-T and T-B-U), we can use the following relationship:
\[ \text{Measure of } S-B-U = \text{Measure of } S-B-T + \text{Measure of } T-B-U \]
Substituting the known values:
\[ 50^\circ = \text{Measure of } S-B-T + 35^\circ \]
Now, we can solve for the measure of angle S-B-T:
\[ \text{Measure of } S-B-T = 50^\circ - 35^\circ = 15^\circ \]
Thus, the measure of angle S-B-T is \( \boxed{15} \) degrees.