To solve for the angle $x$ in the given triangle, we can use the fact that the sum of the angles in any triangle is always 180°.

From the image, we have the following angles:

• One angle is $15^\circ$,
• Another is $30^\circ$,
• The remaining angle is $x$.

So, we can set up the equation:

$15^\circ + 30^\circ + x = 180^\circ$

Now, solve for $x$:

$45^\circ + x = 180^\circ$ $x = 180^\circ - 45^\circ$ $x = 135^\circ$

Thus, the value of $x$ is $135^\circ$.

Would you like further details on solving triangles, or do you have other questions about geometry?

Here are some related questions:

1. How can you apply the Law of Sines or Cosines to solve for unknown angles in non-right triangles?
2. What are the properties of an isosceles triangle in terms of angles and sides?
3. How do you solve for missing side lengths using trigonometry in a right triangle?
4. What is the sum of the interior angles in a polygon, and how do you calculate it?
5. How does the concept of supplementary and complementary angles apply in geometric problems?

Tip: Always check the sum of angles in a triangle as a quick verification after solving!