The document contains a variety of geometry, algebra, and word problems. Here's a summary of the types of problems provided:

1. Triangle Geometry:

   • Range of values for $x$ in a triangle.
   • Find $x$ and the longest side.

2. Exterior and Interior Angles:

   • Proving relationships between exterior and interior angles in polygons.

3. Circle Geometry:

   • Finding angles using tangent properties and circle theorems.

4. Rectangular Geometry:

   • Solve for $x$ in terms of perimeter, involving quadratic expressions.

5. Algebraic Equation:

   • Solve a non-linear equation involving $y$.

6. Phone Plan Cost Comparison:

   • Comparing two phone plans and determining at what cost the plans are equivalent.

7. Garden Dimensions:

   • Using perimeter to determine dimensions of a rectangular garden.

8. Line Intersection and Area:

   • Find the area of a region enclosed by specific lines.

9. Swimming Pool Tiling:

   • Calculating the perimeter of a rectangular pool based on tile information.

10. Currency Conversion:

    • Writing an equation for currency conversion and applying it to scenarios.

11. Travel and Speed Graphs:

    • Graphing and analyzing speed/distance data over time.

12. Journey Time Analysis:

    • Calculating distances and constructing a distance-time graph based on varying speeds.

Would you like to go through a specific question in detail or solve one of these problems? Let me know!