To find the value of $x$, we analyze the figure step by step.

Observations:

1. The triangle markings:

   • The two sides with identical marks indicate that this is an isosceles triangle.
   • This means the two base angles are congruent.

2. Angle relationships:

   • The given triangle has three angles:
     • One base angle is $29^\circ$.
     • The other base angle is also $29^\circ$ (by the isosceles triangle property).
     • The vertex angle (top angle) is $x^\circ$.

3. Sum of angles in a triangle:
   The sum of all internal angles in any triangle is $180^\circ$.

Step-by-step Solution:

1. Write the equation for the sum of angles:
   $x + 29^\circ + 29^\circ = 180^\circ$

2. Simplify the equation:
   $x + 58^\circ = 180^\circ$

3. Solve for $x$:
   $x = 180^\circ - 58^\circ$ $x = 122^\circ$

Final Answer:

$x = 122^\circ$

Would you like me to explain any step in more detail?

Related Questions:

1. What is an isosceles triangle, and how do its angles relate?
2. How do you determine the vertex angle in an isosceles triangle?
3. Can you generalize the sum of angles in any polygon?
4. What happens to the base angles if the vertex angle changes?
5. How do you prove that two angles are congruent in an isosceles triangle?

Tip:

In isosceles triangles, always remember the base angles are equal, and the sum of all angles is $180^\circ$.