The image shows a question about an isosceles triangle. Here's how to solve it step by step:

Step-by-step Solution:

1. Identify the properties of an isosceles triangle:

   • An isosceles triangle has two sides of equal length.
   • The base angles (angles opposite the equal sides) are also equal.

2. Given data:

   • The triangle in the image is isosceles, and $\angle 1$ and $\angle 2$ are the base angles.
   • The vertex angle at the top (let's call it $\angle 3$) is not labeled, but it is part of the triangle.

3. Relationship between angles in a triangle:

   • The sum of all angles in a triangle is always $180^\circ$. That is: $\angle 1 + \angle 2 + \angle 3 = 180^\circ$

4. What to solve:

   • Determine the measures of $\angle 1$ and $\angle 2$, assuming we know $\angle 3$ or have additional context about the measures.

5. If more information is given:

   • If $\angle 3$ (the vertex angle) is specified, subtract it from $180^\circ$ and divide the remaining value equally between $\angle 1$ and $\angle 2$ because they are equal.

If you'd like to clarify the measure of $\angle 3$ or have any other details to share, let me know! Would you like a more detailed walkthrough?

Here are 5 questions to expand your understanding:

1. How do we calculate the base angles of an isosceles triangle when only the vertex angle is known?
2. What properties differentiate isosceles triangles from other types of triangles?
3. How can you use algebra to solve for unknown angles in any triangle?
4. Why is the sum of a triangle's angles always $180^\circ$?
5. How do you verify your answers when solving geometry problems?

Tip: Always remember the triangle angle-sum rule ($\angle 1 + \angle 2 + \angle 3 = 180^\circ$) when solving for unknown angles!