Answer: 194 degrees
From the given figure, we can see a transversal forming between the pairs of parallel lines.
Let us focus on the lines n, a, and e. Here, we can see a pair of parallel lines a and e, cut by a transversal n.
We are given a measurement for angle 4, which is 97. Then we are asked to find the sum of angle 2 and angle 4.
One theorem with respect to transversals that we must be familiar with is the Alternate Interior Angles Theorem which states that:
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
With this, we can see from the figure that angle 2 and angle 4 are actually alternate interior angles.
Since they are alternate interior angles, and they are congruent, this would mean that angle 2 also measures 97.
[tex]m\angle4=97;m\angle2=97[/tex]
With this, we can now add the two measurements, and that would give us:
[tex]97+97=194[/tex]
The sum of angle 2 and angle 4 is 194 degrees.
