Given the following non-regular pentagon find the measure of the unknown angle. 144° I= 48° 145 151 > Next Question degrees

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
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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.
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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