Let's go through each polygon and calculate the missing angles step by step:

1. Figure 1: This is a quadrilateral. The sum of the interior angles of a quadrilateral is 360°. $135^\circ + 60^\circ + 50^\circ + x = 360^\circ$ Solving for $x$: $x = 360^\circ - (135^\circ + 60^\circ + 50^\circ) = 360^\circ - 245^\circ = 115^\circ$

2. Figure 2: This is also a quadrilateral. The sum of the angles should equal 360°. $90^\circ + 50^\circ + x + 90^\circ = 360^\circ$ Solving for $x$: $x = 360^\circ - (90^\circ + 50^\circ + 90^\circ) = 360^\circ - 230^\circ = 130^\circ$

3. Figure 3: This is a triangle, and the sum of the interior angles of a triangle is 180°. $60^\circ + x + x = 180^\circ$ Solving for $x$: $2x = 180^\circ - 60^\circ = 120^\circ \implies x = \frac{120^\circ}{2} = 60^\circ$

4. Figure 4: This is a heptagon (7-sided polygon). The sum of the interior angles of a heptagon is: $(7-2) \times 180^\circ = 5 \times 180^\circ = 900^\circ$ Adding up the given angles: $130^\circ + 138^\circ + 122^\circ + 130^\circ + 120^\circ + 130^\circ + x = 900^\circ$ Solving for $x$: $x = 900^\circ - (130^\circ + 138^\circ + 122^\circ + 130^\circ + 120^\circ + 130^\circ) = 900^\circ - 770^\circ = 130^\circ$

5. Figure 5: This is a quadrilateral. The sum of the interior angles is 360°. $120^\circ + 107^\circ + 70^\circ + x = 360^\circ$ Solving for $x$: $x = 360^\circ - (120^\circ + 107^\circ + 70^\circ) = 360^\circ - 297^\circ = 63^\circ$

6. Figure 6: This is another quadrilateral. The sum of the interior angles is 360°. $50^\circ + 90^\circ + 140^\circ + x = 360^\circ$ Solving for $x$: $x = 360^\circ - (50^\circ + 90^\circ + 140^\circ) = 360^\circ - 280^\circ = 80^\circ$

7. Figure 7: This is a quadrilateral, and the sum of the interior angles is 360°. $60^\circ + 60^\circ + 120^\circ + x = 360^\circ$ Solving for $x$: $x = 360^\circ - (60^\circ + 60^\circ + 120^\circ) = 360^\circ - 240^\circ = 120^\circ$

8. Figure 8: This is a quadrilateral (specifically a rhombus). The sum of the interior angles is 360°. $140^\circ + 140^\circ + 40^\circ + x = 360^\circ$ Solving for $x$: $x = 360^\circ - (140^\circ + 140^\circ + 40^\circ) = 360^\circ - 320^\circ = 40^\circ$

Final Answers:

1. $x = 115^\circ$
2. $x = 130^\circ$
3. $x = 60^\circ$
4. $x = 130^\circ$
5. $x = 63^\circ$
6. $x = 80^\circ$
7. $x = 120^\circ$
8. $x = 40^\circ$

Let me know if you'd like more details or have any questions!

Here are five related questions:

1. What is the formula for finding the sum of the interior angles of any polygon?
2. How do you calculate the exterior angles of a polygon?
3. What is the sum of the interior angles of a hexagon (6-sided polygon)?
4. How can we use the properties of regular polygons to find the value of their interior angles?
5. What is the relationship between the interior and exterior angles of polygons?

Tip: Always remember that the sum of the interior angles of a polygon is given by the formula $(n-2) \times 180^\circ$, where $n$ is the number of sides of the polygon.