To solve the problem, we analyze the provided diagram step by step. The goal is to find the measure of the angle marked with a question mark (?). Here's the analysis:

Observations from the diagram:

1. The triangle is isosceles (green sides are equal, marked with the same symbol).
2. The black line inside the triangle splits the base into two equal segments (blue tick marks indicate congruence).
3. Two known angles at the bottom are given as $24^\circ$ and $48^\circ$.

Solution:

Step 1: Sum of angles in a triangle

For any triangle, the sum of its interior angles is $180^\circ$. Let the apex angle of the larger isosceles triangle (green triangle) be $x$. Then: $x + 24^\circ + 48^\circ = 180^\circ$ $x = 180^\circ - 72^\circ = 108^\circ$

Step 2: Apex angle of the isosceles triangle

The apex angle ($108^\circ$) is split by the black line into two equal parts because the triangle is isosceles. Each half of the apex angle is: $\text{Each part} = \frac{108^\circ}{2} = 54^\circ$

Step 3: Finding the required angle

The angle marked as $?$ is supplementary to one of these $54^\circ$ angles (together they form a straight line). Thus: $\text{Angle } ? = 180^\circ - 54^\circ = 126^\circ$

Final Answer:

The angle marked with the question mark is: $\boxed{126^\circ}$

Let me know if you'd like further clarification or a breakdown of any step! 😊

Related Questions:

1. How do you calculate angles in isosceles triangles?
2. Why does the apex angle split evenly in this case?
3. How can we confirm the supplementary property of the marked angle?
4. What are the rules of angle sums in polygons beyond triangles?
5. How would the solution change if the bottom angles were different?

Tip:

Always check for symmetry or equal segments in diagrams; they often simplify calculations!