Hi!
Let's look at the angle diagonal from 45 degrees. Angles opposite from each other divided by 2 straight lines are vertical angles. They are always equal.
Therefore, that angle is also 45 degrees.
Now, we have one missing angle in the triangle on the left. Triangles add up to 180 degrees, so:
180 - 45 - 60 = 75
That angle is 75 degrees.
Now, we have three angles on a straight line (75 degree angle, 68 degree angle, and missing angle). Angles on a straight line like this are supplementary angles and always add up to 180 degrees.
Therefore:
180 - 75 - 68 =37
The angle is 37 degrees.
Now, we have one missing angle in the triangle on the right. Like said before, triangles add up to 180 degrees, so:
180 - 37 - 100 = 43
The angle is 43 degrees.
Now, we once again have supplementary angles, because we can extend the straight line farther to the right. They add up to 180 degrees, so:
180 - 43 = 137
Now, we once again have vertical angles. This means that the angle opposite of the 137 degree angle will also be 137 degrees, and that's x!
Therefore, x = 137 degrees
See image below for the angles we solved for.