From the image, we see a triangle with one of its angles marked as $91^\circ$ and another angle labeled as $x^\circ$. The triangle also has two congruent sides, which are marked by similar ticks. This indicates that it is an isosceles triangle, where the two base angles are equal.

To find $x$, we use the property that the sum of the interior angles of a triangle is always $180^\circ$. Let's set up the equation:

$91^\circ + x^\circ + x^\circ = 180^\circ$

Simplifying the equation:

$91^\circ + 2x^\circ = 180^\circ$

Now, solve for $x$:

$2x^\circ = 180^\circ - 91^\circ$ $2x^\circ = 89^\circ$ $x^\circ = \frac{89^\circ}{2}$ $x^\circ = 44.5^\circ$

Thus, the value of $x$ is $44.5^\circ$.

Would you like further clarification or a deeper explanation of any part of this solution?

Here are 5 related questions to consider:

1. How do you prove that the angles in a triangle always add up to 180°?
2. What is the general property of angles in an isosceles triangle?
3. How would you approach solving for angles in other types of triangles?
4. How does symmetry in geometric shapes help simplify problems like this one?
5. Can you solve for the length of a side in an isosceles triangle if you know the angles?

Tip: Always check for congruent sides or angles when solving triangle problems, as this can simplify the solution!