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.