### Polygon Angle ProblemIn this problem, you are given a polygon with the following internal angles:- 116°- 135°- 136°- 164°- 101°- 139°- 151°- One unknown angle \( x \)Your task is to determine the value of \( x \).#### Step-by-Step Solution:1. **Identify the Polygon**: This is an octagon since it has eight sides.2. **Sum of Internal Angles**: The formula for the sum of the internal angles of an \( n \)-sided polygon is: \[ (n - 2) \times 180^\circ \] For an octagon (\( n = 8 \)): \[ (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ \]3. **Sum Given Angles and Set Up the Equation**: Add the given angles together: \[ 116^\circ + 135^\circ + 136^\circ + 164^\circ + 101^\circ + 139^\circ + 151^\circ = 942^\circ \] The sum of the given angles plus \( x \) should equal the total sum of internal angles of the octagon: \[ 942^\circ + x = 1080^\circ \]4. **Solve for \( x \)**: \[ x = 1080^\circ - 942^\circ = 138^\circ \]Thus, the value of \( x \) is \( 138^\circ \).### Question:What is the value of \( x \)?### Answer:The value of \( x \) is \( 138^\circ \).

Name: ### Polygon Angle ProblemIn this problem, you are given a polygon wit
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: ### Polygon Angle ProblemIn this problem, you are given a polygon with the following internal angles:- 116°- 135°- 136°- 164°- 101°- 139°- 151°- One unknown angle \( x \)Your task is to determine the value of \( x \).#### Step-by-Step Solution:1. **