https://file.aiquickdraw.com/mathbot/file/1727355252743bl6dk8m5.jpg

The image you provided contains a diagram and a question about a pentagon. Let me explain the situation:

### Problem Context:
- The shape **PORST** is a regular pentagon.
- **QPU**, **RVU**, and **STU** are straight lines, as noted in the diagram.
- A calculation is shown that involves determining angles related to this pentagon.

### Explanation of the Work on the Image:
1. **Formula for interior angles of a polygon**:
   The sum of the interior angles of a polygon is given by the formula:
   \[
   \text{Sum of interior angles} = (n - 2) \times 180^\circ
   \]
   where \( n \) is the number of sides of the polygon.

2. **Applying to a pentagon**:
   Since a pentagon has 5 sides, the sum of its interior angles is:
   \[
   (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
   \]
   Each interior angle of a regular pentagon is therefore:
   \[
   \frac{540^\circ}{5} = 108^\circ
   \]
   This is what is written down in the image.

3. **Other calculations**:
   - The work \( x + 108^\circ = 180^\circ \) indicates the calculation of angle \( x \), which is supplementary to the pentagon angle of \( 108^\circ \) (meaning their sum is \( 180^\circ \)).
   - Solving this gives \( x = 180^\circ - 108^\circ = 72^\circ \).

Thus, the angle \( x \) in this problem is \( 72^\circ \), which aligns with the geometry of the pentagon and straight lines mentioned in the question.

### Would you like further details or clarification?

Here are 5 related questions to explore this topic further:
1. What is the formula for the exterior angles of a regular polygon?
2. How can we calculate the sum of the interior angles of any polygon?
3. What are the properties of a regular pentagon besides equal sides and angles?
4. How do supplementary and complementary angles work in different polygons?
5. Can the angle sum formula be extended to non-convex polygons?

**Tip**: Always verify if a polygon is regular (equal sides and angles) before applying the equal angle formula.

Dalam rajah di bawah, PORST ialah pentagon sekata. QPU, RVU dan STU ialah garis lurus.

Understand how to calculate the interior angles of a regular pentagon and solve for unknown angles using supplementary angle properties. The problem covers polygon angle formulas and the angle sum property, suitable for students in Grades 8-10.

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