Test I - Instructions: Give what are asked in each box where specific measure of angle of an irregular polygon is missing. Provide your solution to the right-side space of each box for additional points.

Number of sides (n):

Sum of interior angles

(S

Measure of x°:

Solution:

154°

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

125°

1179

68°

79°

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

0124160°

0120°

x°

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

118°

124°

140°

148° x°

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

147°

102°

10° C

128

138

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

118°

150°

124°

80°

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

122°

130°

130°

130°

138°

128°

Number of sides (n):

Sum of interior angles (S):

Measure of x°:

Solution:

130°

125°

160°

150°

150°

120°

140°


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.

Explore how to find missing angles in irregular polygons with detailed examples and step-by-step solutions. Understand the sum of interior angles formula and its application in solving geometry problems. Suitable for high school students studying geometry.

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