To solve this problem, we need to determine the sum of the interior angles for each polygon formed by the given vertices and match them with the correct expression. The formula to find the sum of the interior angles of a polygon is:

$\text{Sum of interior angles} = (n - 2) \times 180^\circ$

Where $n$ is the number of sides of the polygon.

Let's calculate the sum of interior angles for each polygon:

1. Polygon PORSTUVW:

   • This polygon has 7 sides (P, O, R, S, T, U, W).
   • Sum of interior angles = $(7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ$.

2. Polygon PRSTU:

   • This polygon has 5 sides (P, R, S, T, U).
   • Sum of interior angles = $(5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$.

3. Polygon PSTUVWX:

   • This polygon has 7 sides (P, S, T, U, V, W, X).
   • Sum of interior angles = $(7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ$.

4. Polygon PTUVW:

   • This polygon has 6 sides (P, T, U, V, W, X).
   • Sum of interior angles = $(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$.

Now let's match each polygon to the correct sum of interior angles:

• PORSTUVW: 5 × 180° = 900°
• PRSTU: 3 × 180° = 540°
• PSTUVWX: 5 × 180° = 900°
• PTUVW: 4 × 180° = 720°

The correct matching is:

• PORSTUVW matches with 5 × 180°.
• PRSTU matches with 3 × 180°.
• PSTUVWX matches with 5 × 180°.
• PTUVW matches with 4 × 180°.

Would you like further clarification or have any additional questions?

Here are 5 related questions you might consider:

1. How does the formula for the sum of interior angles change if the polygon has more than 10 sides?
2. What is the sum of the exterior angles of any polygon, regardless of the number of sides?
3. How can you determine the measure of each interior angle if the polygon is regular?
4. What is the difference in the sum of interior angles between a 7-sided polygon and a 9-sided polygon?
5. How does the sum of interior angles relate to the sum of exterior angles for any polygon?

Tip: Remember that the sum of interior angles increases by 180° for each additional side added to a polygon.