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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.

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Learn how to solve for the unknown angle in a triangle using the triangle angle sum theorem. This problem involves angles 33°, 45°, and x, where the sum of all angles equals 180°. Suitable for students in Grades 6-8.

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