To solve for $x^\circ$ in the given triangle, we can use the fact that the sum of the interior angles in any triangle is always $180^\circ$.

The angles given in the triangle are:

• $x^\circ$
• $33^\circ$
• $45^\circ$

The equation to solve for $x$ is:

$x + 33^\circ + 45^\circ = 180^\circ$

Simplifying:

$x + 78^\circ = 180^\circ$

Now, subtract $78^\circ$ from both sides:

$x = 180^\circ - 78^\circ$

$x = 102^\circ$

Thus, the value of $x$ is $102^\circ$.

Would you like more details on this, or do you have any questions?

Related Questions:

1. What is the sum of the exterior angles of any polygon?
2. Can a triangle have two angles greater than $90^\circ$?
3. What is the smallest possible value for an interior angle in a triangle?
4. How can you verify that a triangle is valid using its angles?
5. What is the name of a triangle where all angles are less than $90^\circ$?

Tip: The sum of interior angles of any polygon can be determined using the formula $180(n-2)$, where $n$ is the number of sides.