**Title: Solving for Unknown Angles in a Polygon** **Objective:** Determine the unknown angle \( x \) in a given polygon. **Diagram:** The diagram represents a pentagon with the following angles: - One angle is 100° - One angle is 120° - One angle is 90° - One angle is 108° - The unknown angle is denoted as \( x \). **Problem:** Calculate the value of \( x \). **Solution Process:** To find \( x \), use the formula for the sum of the interior angles of a polygon: 1. Determine the sum of all interior angles of a pentagon: \[ \text{Sum of angles} = (5-2) \times 180° = 540° \] 2. Add the known angles: \[ 100° + 120° + 90° + 108° = 418° \] 3. Subtract the sum of the known angles from the total sum to find \( x \): \[ x = 540° - 418° = 122° \] **Answer Choices:** - 58° - 108° - 122° (Correct Answer) - 180° This method provides a clear understanding of how to calculate unknown angles in polygons using known interior angles and the sum formula.
**Title: Solving for Unknown Angles in a Polygon** **Objective:** Determine the unknown angle \( x \) in a given polygon. **Diagram:** The diagram represents a pentagon with the following angles: - One angle is 100° - One angle is 120° - One angle is 90° - One angle is 108° - The unknown angle is denoted as \( x \). **Problem:** Calculate the value of \( x \). **Solution Process:** To find \( x \), use the formula for the sum of the interior angles of a polygon: 1. Determine the sum of all interior angles of a pentagon: \[ \text{Sum of angles} = (5-2) \times 180° = 540° \] 2. Add the known angles: \[ 100° + 120° + 90° + 108° = 418° \] 3. Subtract the sum of the known angles from the total sum to find \( x \): \[ x = 540° - 418° = 122° \] **Answer Choices:** - 58° - 108° - 122° (Correct Answer) - 180° This method provides a clear understanding of how to calculate unknown angles in polygons using known interior angles and the sum formula.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
100%
Solve for x,
interior
![**Title: Solving for Unknown Angles in a Polygon**
**Objective:**
Determine the unknown angle \( x \) in a given polygon.
**Diagram:**
The diagram represents a pentagon with the following angles:
- One angle is 100°
- One angle is 120°
- One angle is 90°
- One angle is 108°
- The unknown angle is denoted as \( x \).
**Problem:**
Calculate the value of \( x \).
**Solution Process:**
To find \( x \), use the formula for the sum of the interior angles of a polygon:
1. Determine the sum of all interior angles of a pentagon:
\[
\text{Sum of angles} = (5-2) \times 180° = 540°
\]
2. Add the known angles:
\[
100° + 120° + 90° + 108° = 418°
\]
3. Subtract the sum of the known angles from the total sum to find \( x \):
\[
x = 540° - 418° = 122°
\]
**Answer Choices:**
- 58°
- 108°
- 122° (Correct Answer)
- 180°
This method provides a clear understanding of how to calculate unknown angles in polygons using known interior angles and the sum formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ca575c3-e7a0-4200-8af2-09dad4314965%2F5b3b3f87-238b-4bf2-a577-dac74f4fe053%2Fgf3pxt8.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving for Unknown Angles in a Polygon**
**Objective:**
Determine the unknown angle \( x \) in a given polygon.
**Diagram:**
The diagram represents a pentagon with the following angles:
- One angle is 100°
- One angle is 120°
- One angle is 90°
- One angle is 108°
- The unknown angle is denoted as \( x \).
**Problem:**
Calculate the value of \( x \).
**Solution Process:**
To find \( x \), use the formula for the sum of the interior angles of a polygon:
1. Determine the sum of all interior angles of a pentagon:
\[
\text{Sum of angles} = (5-2) \times 180° = 540°
\]
2. Add the known angles:
\[
100° + 120° + 90° + 108° = 418°
\]
3. Subtract the sum of the known angles from the total sum to find \( x \):
\[
x = 540° - 418° = 122°
\]
**Answer Choices:**
- 58°
- 108°
- 122° (Correct Answer)
- 180°
This method provides a clear understanding of how to calculate unknown angles in polygons using known interior angles and the sum formula.
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