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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![**Problem: Finding the Unknown Angle in a Non-Regular Pentagon**
**Description:**
Given the following non-regular pentagon, find the measure of the unknown angle.
The pentagon has the following interior angles labeled:
- 48°
- 144°
- 151°
- 145°
- \( x^\circ \) (unknown angle)
**Diagram Explanation:**
The diagram shows a five-sided polygon, with the interior angles labeled as specified above. The shape is irregular, meaning its sides and angles are not all equal.
**Calculation Task:**
To find the measure of angle \( x \), use the formula for the sum of interior angles of a pentagon. The sum of the interior angles in any pentagon is:
\[ (5 - 2) \times 180^\circ = 540^\circ \]
Therefore, calculate:
\[ 48^\circ + 144^\circ + 151^\circ + 145^\circ + x = 540^\circ \]
Simplify to solve for \( x \):
\[ x = 540^\circ - (48^\circ + 144^\circ + 151^\circ + 145^\circ) \]
**Input Box:**
\( x = \_\_^\circ \) [Enter the value for \( x \)]
**Navigation:**
- [Next Question] Button to proceed once the calculation is complete.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c22293a-3ae6-4ac2-9c37-c12acd82a0e8%2Fcc03b32f-f0fa-41a8-b4c0-481d3af08f04%2Fwcs6g7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Finding the Unknown Angle in a Non-Regular Pentagon**
**Description:**
Given the following non-regular pentagon, find the measure of the unknown angle.
The pentagon has the following interior angles labeled:
- 48°
- 144°
- 151°
- 145°
- \( x^\circ \) (unknown angle)
**Diagram Explanation:**
The diagram shows a five-sided polygon, with the interior angles labeled as specified above. The shape is irregular, meaning its sides and angles are not all equal.
**Calculation Task:**
To find the measure of angle \( x \), use the formula for the sum of interior angles of a pentagon. The sum of the interior angles in any pentagon is:
\[ (5 - 2) \times 180^\circ = 540^\circ \]
Therefore, calculate:
\[ 48^\circ + 144^\circ + 151^\circ + 145^\circ + x = 540^\circ \]
Simplify to solve for \( x \):
\[ x = 540^\circ - (48^\circ + 144^\circ + 151^\circ + 145^\circ) \]
**Input Box:**
\( x = \_\_^\circ \) [Enter the value for \( x \)]
**Navigation:**
- [Next Question] Button to proceed once the calculation is complete.
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