To find the value of $x$, let’s analyze the diagram provided.

This is a problem involving angles around a point, and the sum of these angles should equal $360^\circ$.

In the diagram, we have three given angles:

1. $x$
2. $34^\circ$
3. $3x$
4. $22^\circ$

Setting up the equation, we can add these angles and set the sum equal to $360^\circ$:

$x + 34^\circ + 3x + 22^\circ = 360^\circ$

Now, combine like terms:

$4x + 56^\circ = 360^\circ$

Subtract $56^\circ$ from both sides:

$4x = 304^\circ$

Now, divide by 4:

$x = 76^\circ$

Answer:

The value of $x$ is $76^\circ$.

Would you like further details or have any questions?

Here are some related questions for practice:

1. What would the value of $x$ be if one of the other angles was changed?
2. How would you approach this problem if it were an equation involving supplementary angles?
3. What if there were four angles around the point, and their sum was different?
4. How can this method be applied to find unknown angles in polygons?
5. Why does the sum of angles around a point equal $360^\circ$?

Tip: When solving for unknowns in angle problems, always look for the sum of angles rules (e.g., around a point, in a triangle) to set up your equation.