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
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![### Geometry Problem: Finding the Value of x
**Problem Statement:**
In the given diagram, several angles of a polygon are provided. Your task is to find the value of the unknown angle marked as \( x \).
**Given:**
- The measure of the angles next to \( x \) are 60°, 30°, 72°, 46°, and 55°.
**Diagram Description:**
The diagram is a pentagon with angles at each vertex. The angles provided in the diagram are:
- One angle is marked with a small blue arc and labeled as 55°.
- Another angle adjacent to it is marked with another small blue arc and labeled as 46°.
- Continuing in a clockwise direction, the next angles are marked as 72°, 30°, and 60°.
- One angle is marked as \( x \), which is the unknown that needs to be determined.
**Choices:**
- \( x \) can be:
- 67°
- 77°
- 87°
- 97°
**Procedure to Find \( x \):**
1. **Sum of Interior Angles of a Polygon:**
For a polygon with \( n \) sides, the sum of the interior angles is given by the formula:
\[
180^\circ \times (n - 2)
\]
Since this is a pentagon (\( n = 5 \)):
\[
180^\circ \times (5 - 2) = 540^\circ
\]
2. **Sum of Known Angles:**
Summing up the given angles:
\[
55^\circ + 46^\circ + 72^\circ + 30^\circ + 60^\circ = 263^\circ
\]
3. **Find \( x \):**
To find the unknown angle \( x \):
\[
540^\circ - 263^\circ = 277^\circ
\]
Therefore, the value of \( x \) must be 97°.
**Answer:**
\[ x = 97^\circ \]
**Options:**
- 67°
- 77°
- 87°
- **97°**
The correct answer is 97°.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47897a37-2eac-43d5-a731-3aff060a1d87%2F7bf3d78c-5a8d-44d3-9e94-687156ff7180%2Fsdhbfpe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding the Value of x
**Problem Statement:**
In the given diagram, several angles of a polygon are provided. Your task is to find the value of the unknown angle marked as \( x \).
**Given:**
- The measure of the angles next to \( x \) are 60°, 30°, 72°, 46°, and 55°.
**Diagram Description:**
The diagram is a pentagon with angles at each vertex. The angles provided in the diagram are:
- One angle is marked with a small blue arc and labeled as 55°.
- Another angle adjacent to it is marked with another small blue arc and labeled as 46°.
- Continuing in a clockwise direction, the next angles are marked as 72°, 30°, and 60°.
- One angle is marked as \( x \), which is the unknown that needs to be determined.
**Choices:**
- \( x \) can be:
- 67°
- 77°
- 87°
- 97°
**Procedure to Find \( x \):**
1. **Sum of Interior Angles of a Polygon:**
For a polygon with \( n \) sides, the sum of the interior angles is given by the formula:
\[
180^\circ \times (n - 2)
\]
Since this is a pentagon (\( n = 5 \)):
\[
180^\circ \times (5 - 2) = 540^\circ
\]
2. **Sum of Known Angles:**
Summing up the given angles:
\[
55^\circ + 46^\circ + 72^\circ + 30^\circ + 60^\circ = 263^\circ
\]
3. **Find \( x \):**
To find the unknown angle \( x \):
\[
540^\circ - 263^\circ = 277^\circ
\]
Therefore, the value of \( x \) must be 97°.
**Answer:**
\[ x = 97^\circ \]
**Options:**
- 67°
- 77°
- 87°
- **97°**
The correct answer is 97°.
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