To find the value of $x$ in this circle diagram, let's analyze the information given:

1. The sum of the angles around a point (the center of the circle) is $360^\circ$.
2. We know two of the angles around this point:
   • One angle is $145^\circ$.
   • Another angle is a right angle, which is $90^\circ$.
3. Let $x$ be the third angle.

Since these angles must add up to $360^\circ$, we can set up the equation: $145^\circ + 90^\circ + x = 360^\circ$

Now, we solve for $x$: $235^\circ + x = 360^\circ$ $x = 360^\circ - 235^\circ$ $x = 125^\circ$

So, the value of $x$ is $125^\circ$.

Would you like a detailed explanation of any part of this process, or do you have further questions?

Here are some related questions that might interest you:

1. How do we know that the angles around a point sum to $360^\circ$?
2. What are some common properties of central angles in a circle?
3. How would this change if the circle had four or more sectors?
4. Can this method be applied to find missing angles in polygons?
5. How do right angles affect calculations in circular diagrams?

Tip: Remember, in a circle, the angles around the center always add up to $360^\circ$, which is a useful fact for solving problems like these!