please help ### 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°.

Name: please help ### Geometry Problem: Finding the Value of x**Problem Stat
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Description: please help ### 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

Answered: 24. Find the value of x. 60° 30° to 72…

Math

Geometry

24. Find the value of x. 60° 30° to 72 55 46 O 67 O 77 87 O 97

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°.

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