To solve for $x$ in this triangle problem, we will use the following steps:

Step 1: Understand the Triangle

From the image:

• One angle of the triangle is $21^\circ$,
• Another angle is $34^\circ$,
• The third angle is $x^\circ$ (unknown).

The sum of angles in any triangle equals $180^\circ$.

Step 2: Set Up the Equation

$x + 21^\circ + 34^\circ = 180^\circ$

Step 3: Solve for $x$

Combine the known angles: $x + 55^\circ = 180^\circ$

Subtract $55^\circ$ from both sides: $x = 180^\circ - 55^\circ$

$x = 125^\circ$

Final Answer:

$x = 125^\circ$

Let me know if you'd like additional explanations or details!

Here are five related questions to deepen your understanding:

1. What is the sum of the interior angles of a quadrilateral?
2. How can we determine if a triangle is acute, obtuse, or right from its angles?
3. How do supplementary angles relate to triangles?
4. Can you identify the type of triangle (acute, obtuse, right) based on this solution?
5. What happens to the angles of a triangle if one side lengthens or shortens?

Tip: Always remember that the sum of the angles in a triangle is $180^\circ$, no matter the type of triangle!