The figure below shows BT with point B at the intersection of SW and RU.

Lines S-W and R-U intersect at B to form four angles R-B-S, S-B-U, U-B-W, and W-B-R. The line B-T divides the angle S-B-U into two angles S-B-T and T-B-U. The measure of T-B-U is 35 degrees, and the measure of R-B-W is 130 degrees.

What is the measure of SBT ?

1 answer

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.