Question 41
Úrsula drew a convex polygon with sides $11$ and called its vertices $A_1, A_2, A_3, A_4, A_5, A_6, A_7, A_8, A_9, A_{10}$ and $A_{11}$. Then he drew some diagonals of the polygon (such that any two did not intersect inside the polygon) until the polygon was divided into triangles.
For each vertex, he counted how many triangles that vertex belonged to and recorded that number in a table.
Úrsula's table, from which three numbers have been deleted, is:
| $A_1$ | $A_2$ | $A_3$ | $A_4$ | $A_5$ | $A_6$ | $A_7$ | $A_8$ | $A_9$ | $A_{10}$ | $A_{11}$ |
|-------|-------|-------|-------|-------|-------|-------|-------|-------|----------|----------|
| 4 | 2 | 3 | | 2 | 5 | | 3 | 3 | | 2 |
Draw the diagonals that Úrsula had drawn in a convex polygon $A_1A_2A_3A_4A_5A_6A_7A_8A_9A_{10}A_{11}$.
For each vertex, he counted how many triangles that vertex belonged to and recorded that number in a table.
Úrsula's table, from which three numbers have been deleted, is:
| $A_1$ | $A_2$ | $A_3$ | $A_4$ | $A_5$ | $A_6$ | $A_7$ | $A_8$ | $A_9$ | $A_{10}$ | $A_{11}$ |
|-------|-------|-------|-------|-------|-------|-------|-------|-------|----------|----------|
| 4 | 2 | 3 | | 2 | 5 | | 3 | 3 | | 2 |
Draw the diagonals that Úrsula had drawn in a convex polygon $A_1A_2A_3A_4A_5A_6A_7A_8A_9A_{10}A_{11}$.