To find the value of $x$, let's analyze the diagram:

Step 1: Identify the relevant angles

• The triangle in the diagram has an exterior angle of $97^\circ$ and an interior angle of $51^\circ$ next to it.
• The angle $x$ is the other interior angle of the triangle.

Step 2: Use the triangle exterior angle property

The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Mathematically: $97^\circ = x + 51^\circ$

Step 3: Solve for $x$

To find $x$, subtract $51^\circ$ from $97^\circ$: $x = 97^\circ - 51^\circ$ $x = 46^\circ$

Final Answer:

The value of $x$ is $46^\circ$.

Do you need further clarification or additional details?

Here are some related questions to deepen your understanding:

1. How do you prove that the exterior angle of a triangle equals the sum of the two opposite interior angles?
2. What is the sum of all interior angles in a triangle?
3. Can you solve for missing angles in a triangle using other methods, such as supplementary angles?
4. What happens to the exterior angle property in non-triangular polygons?
5. How do adjacent angles (like $97^\circ$ and its neighbor) relate to each other in geometry?

Tip: The sum of interior angles in any triangle is always $180^\circ$. Use this property whenever two angles are known to solve for the third!