This is a triangle problem where we need to find the marked angle. The sum of angles in a triangle is always 180°. Let’s solve it step by step:

1. Identify the known angles:

   • One angle is given as $68.5^\circ$.
   • The two base angles are equal (indicated by their colors and symmetry), so they are both $68.5^\circ$.

2. Calculate the total angle contribution from the two base angles: $68.5^\circ + 68.5^\circ = 137^\circ$

3. Subtract from 180° to find the unknown angle: $180^\circ - 137^\circ = 43^\circ$

Thus, the marked angle is $\boxed{43^\circ}$.

Let me know if you'd like further clarification!

Here are 5 related questions for deeper exploration:

1. Why does the sum of angles in a triangle always equal 180°?
2. What is the relationship between isosceles triangles and their base angles?
3. How can we calculate angles in irregular (scalene) triangles?
4. What is the significance of symmetry in geometric figures like triangles?
5. How can you verify the angles using a protractor?

Tip: Always double-check calculations by verifying the total angle sum of the triangle equals 180°.