Thank you for sharing the details. Let's go through each of these problems step by step to find the solutions. For each problem, we will:

1. Determine the number of sides of the polygon ($n$).
2. Calculate the sum of the interior angles ($S$).
3. Solve for the missing angle $x^\circ$.

Problem 1:

• Number of sides (n):
  • It seems this polygon is not explicitly named, so count the angles or sides if there’s a diagram. However, based on standard geometry, we can consider specific cases such as pentagons, hexagons, etc.
• Sum of interior angles (S):
  • Use the formula: $S = (n - 2) \times 180^\circ$.
• Measure of $x^\circ$:
  • To find $x$, sum the given angles and subtract from the total sum of interior angles $S$.

Problem 2:

Given angles are 125°, 117°, 79°, 68°.

• Number of sides (n): 5 (assuming it's a pentagon)
• Sum of interior angles (S): $S = (5 - 2) \times 180^\circ = 540^\circ$.
• Measure of $x^\circ$:
  • $x^\circ = 540^\circ - (125^\circ + 117^\circ + 79^\circ + 68^\circ)$
  • $x^\circ = 540^\circ - 389^\circ = 151^\circ$

Problem 3:

Given angles are 140°, 148°, 124°, 118°.

• Number of sides (n): 5 (assuming it's a pentagon)
• Sum of interior angles (S): $S = 540^\circ$.
• Measure of $x^\circ$:
  • $x^\circ = 540^\circ - (140^\circ + 148^\circ + 124^\circ + 118^\circ)$
  • $x^\circ = 540^\circ - 530^\circ = 10^\circ$

Problem 4:

Given angles are 118°, 150°, 124°, 80°.

• Number of sides (n): 5 (assuming it's a pentagon)
• Sum of interior angles (S): $S = 540^\circ$.
• Measure of $x^\circ$:
  • $x^\circ = 540^\circ - (118^\circ + 150^\circ + 124^\circ + 80^\circ)$
  • $x^\circ = 540^\circ - 472^\circ = 68^\circ$

Problem 5:

Given angles are 122°, 130°, 130°, 130°, 138°, 128°.

• Number of sides (n): 7 (assuming it's a heptagon)
• Sum of interior angles (S): $S = (7 - 2) \times 180^\circ = 900^\circ$.
• Measure of $x^\circ$:
  • $x^\circ = 900^\circ - (122^\circ + 130^\circ + 130^\circ + 130^\circ + 138^\circ + 128^\circ)$
  • $x^\circ = 900^\circ - 778^\circ = 122^\circ$

Problem 6:

Given angles are 130°, 125°, 160°, 150°, 150°, 120°, 140°.

• Number of sides (n): 8 (assuming it's an octagon)
• Sum of interior angles (S): $S = (8 - 2) \times 180^\circ = 1080^\circ$.
• Measure of $x^\circ$:
  • $x^\circ = 1080^\circ - (130^\circ + 125^\circ + 160^\circ + 150^\circ + 150^\circ + 120^\circ + 140^\circ)$
  • $x^\circ = 1080^\circ - 975^\circ = 105^\circ$

Summary of Answers:

1. $x^\circ$ depends on the first missing data—let me know how many sides there are.
2. $x^\circ = 151^\circ$
3. $x^\circ = 10^\circ$
4. $x^\circ = 68^\circ$
5. $x^\circ = 122^\circ$
6. $x^\circ = 105^\circ$

Let me know if you need any additional details, or if you'd like to clarify or check any specific part of this.

Tip: Always double-check how many sides each polygon has to ensure the accuracy of your calculations.