Let's analyze the given diagram and solve for angle $x$.

Step-by-Step Solution:

1. Identify Angles in the Triangle:

   • In the triangle on the left side, there are three angles. Let's label them based on the image:
     • $2x$ (at the bottom left of the triangle),
     • $x^\circ$ (at the top of the triangle),
     • $x^\circ$ (at the bottom right of the triangle, adjacent to $y^\circ$).

2. Sum of Angles in a Triangle:

   • The sum of the interior angles in a triangle is always $180^\circ$.
   • Therefore, we can write the equation for the triangle as: $2x + x + x = 180^\circ$
   • Simplifying this gives: $4x = 180^\circ$
   • Dividing both sides by 4: $x = 45^\circ$

Thus, the angle $x$ is $45^\circ$.

Would you like a more detailed explanation, or do you have further questions?

Follow-up Questions

1. What is the measure of angle $2x$ given that $x = 45^\circ$?
2. If $y = 32^\circ$, what is the total angle where $x$ and $y$ meet on the right side?
3. How would the solution change if $y$ were a different value?
4. Can we use the exterior angle theorem in this problem?
5. How does this problem illustrate the properties of angle sums in triangles?

Tip:

Always remember that the sum of the interior angles in any triangle is $180^\circ$. This rule is fundamental for solving problems involving unknown angles in triangles.