Question

Use the relationship between the angles in the figure to answer the question.
Which equation can be used to find the value of x? 

Answer 1

Look into my attachment, I named the point so you can easily understand

∠AOB, ∠BOC, ∠COD are supplementary angles
∠AOB + ∠BOC + ∠COD = 180°
28° + ∠BOC + 49° = 180°
∠BOC = 180° - 49° - 28°
∠BOC = 103°

x° and ∠BOC are vertical angles, so the number of those angles is the same
x° = ∠BOC
x° = 103°

Answer 2

Vertical angles (those directly across from each other) are congruent.
This means two angles have a measure of 49 degrees - those across from each other, and two angles have a measure of 28 degrees - also those across from each other.

We also have supplementary angles, which are adjacent angles (angles that share a side) which add to equal 180 degrees. Visualize a straight line with another line going through it at an angle; the pairs of angles it creates are supplementary.

With all that refreshed, we can work out the value of x.

The line going horizontally straight across creates supplementary angles between x and two other angles which we know equal 49 and 28, respectively.

Since supplementary angles add to equal 180 degrees, we can set up the following equation to solve for x:

49 + 28 + x = 180
77 + x = 180
x = 103

Answer:
x = 103