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.