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To find the value of \( x \) in this triangle, we can use the triangle angle sum property. This property states that the sum of the interior angles in a triangle is always \( 180^\circ \).

The triangle has two given angles: \( 45^\circ \) and \( 54^\circ \).

### Solution:
1. Sum of the angles in the triangle:
   \[
   45^\circ + 54^\circ + x = 180^\circ
   \]
2. Combine the known angles:
   \[
   99^\circ + x = 180^\circ
   \]
3. Solve for \( x \) by subtracting \( 99^\circ \) from both sides:
   \[
   x = 180^\circ - 99^\circ
   \]
   \[
   x = 81^\circ
   \]

### Answer:
The value of \( x \) is \( 81^\circ \).

Would you like further details or have any questions?

Here are 5 related questions that build on this concept:
1. How would you find an unknown angle in a triangle if only two angles are given?
2. What is the rule for the sum of angles in a quadrilateral?
3. How would the solution change if this were an obtuse triangle?
4. Can the triangle inequality theorem help determine if these angles form a valid triangle?
5. What are the angle sum properties in polygons with more than three sides?

**Tip:** Remember that in any triangle, the sum of all angles is always \( 180^\circ \). This is a fundamental rule that applies to all types of triangles.

Find the value of x in a triangle with given angles of 45° and 54°.

Learn how to find the missing angle in a triangle where two angles are given as 45° and 54°. This problem covers the triangle angle sum theorem, making it suitable for students in Grades 6-8. Follow a step-by-step approach to determine the unknown angle x.

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