To solve this problem, we use the property of a triangle where the sum of the interior angles equals $180^\circ$.

The angles in this triangle are given as:

• $x$
• $2x$
• $3x$

Step 1: Set up the equation for the sum of the angles

$x + 2x + 3x = 180^\circ$

Step 2: Simplify the equation

$6x = 180^\circ$

Step 3: Solve for $x$

$x = \frac{180^\circ}{6} = 30^\circ$

Final Answer:

$x = 30^\circ$

Would you like me to provide more detailed explanations or assist with a related topic? Here are 5 questions to deepen your understanding:

1. What would the other angles of the triangle measure when $x = 30^\circ$?
2. How does the property of triangle angle sums apply in non-Euclidean geometry?
3. What would change if the angles were expressed in terms of radians?
4. How can you verify your solution using trigonometry?
5. Could this problem be adapted for isosceles or right triangles?

Tip: Always verify the sum of your calculated angles equals $180^\circ$ when solving for unknown angles in triangles.