There are two different ways of calculating the angle $x$.
The first method is as follows:
The blue angle can be calculated since angles on a straight line add to $180^\circ$. This means it is $180^\circ - 100^\circ = 80^\circ$.
The orange angle can be calculated similarly, to be $180^\circ - 93^\circ = 87^\circ$.
The green angle can then be calculated since the angles in the top-left triangle add up to $180^\circ$. This is $180^\circ - 80^\circ - 58^\circ = 42^\circ$.
The green and red angles are opposite angles. This means that they are equal, so the red angle is also $42^\circ$.
Then, the angles in the left-hand triangle must add up to $180^\circ$, so $x^\circ = 180^\circ - 42^\circ - 87^\circ= 51^\circ$.
The other method involves looking at the farthest right angle in the diagram.
The angles in the red and purple triangle must add up to $180^\circ$, so the green angle is $180^\circ - 58^\circ - 93^\circ = 29^\circ$.
Then, the angles in the blue triangle must also add up to $180^\circ$. Therefore, $x^\circ = 180^\circ - 29^\circ - 100^\circ = 51^\circ$.