To find the indicated angle (denoted as $\alpha$) in the figure, we need to analyze the geometry of the given shape. Here's the step-by-step solution:

Step 1: Analyze the Shape

The figure appears to be a pentagon with an external angle labeled as $88^\circ$. The angle $\alpha$ seems to be the internal angle adjacent to this external angle.

Step 2: Relationship Between Internal and External Angles

For any polygon, the external angle and the adjacent internal angle are supplementary, meaning their sum is $180^\circ$. Therefore, the internal angle $\alpha$ can be calculated using:

$\alpha + \text{external angle} = 180^\circ$

Given that the external angle is $88^\circ$:

$\alpha + 88^\circ = 180^\circ$

Step 3: Solve for $\alpha$

Subtract $88^\circ$ from both sides:

$\alpha = 180^\circ - 88^\circ = 92^\circ$

Final Answer

The indicated angle $\alpha$ measures $92^\circ$.

Do you want further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How can you calculate the sum of internal angles in a pentagon?
2. What is the measure of each internal angle in a regular pentagon?
3. How do external and internal angles relate to each other in polygons?
4. Can you derive the formula for the internal angles of an $n$-sided polygon?
5. How would the calculation change if the figure were a hexagon?

Tip: Always remember that internal and external angles at the same vertex of a polygon are supplementary.