Exercise 18 Page 377

Let's consider the given diagram.

We are told that line $s$ is parallel to line $t.$ We are also told the measures of two angles, $m\angle 2=110^{\circ }$ and $m\angle 11=137^{\circ }.$ Let's add this information to our diagram.

To find the measure of $\angle 13,$ we will use the fact that when two lines intersect, vertical angles are formed on opposite sides of the point of intersection, and these angles are always congruent.

Since $\angle 2$ and $\angle 13$ are vertical angles, these angles are congruent.