## Problem 15: Solve for \( x \).### Problem Statement:You are given a quadrilateral with the internal angles defined algebraically. The four angles are denoted as follows:1. Top-left angle: \( (10x + 6)^\circ \)2. Bottom-left angle: \( (13x - 2)^\circ \)3. Bottom-right angle: \( (8x - 1)^\circ \)4. Top-right angle: \( 71^\circ \)### Task:Solve for \( x \).#### Explanation:In a quadrilateral, the sum of all internal angles is always \( 360^\circ \). Therefore, you can set up the following equation using the given angles:\[(10x + 6)^\circ + (13x - 2)^\circ + (8x - 1)^\circ + 71^\circ = 360^\circ\]1. Combine like terms:\[10x + 13x + 8x + 6 - 2 - 1 + 71 = 360\]2. Simplify the equation:\[31x + 74 = 360\]3. Solve for \( x \):\[31x + 74 - 74 = 360 - 74 \\31x = 286 \\x = \frac{286}{31} \\x = 9.23\]Thus, the value of \( x \) is approximately \( 9.23 \).### Conclusion:To solve for \( x \), you recognize that the sum of the internal angles of a quadrilateral is \( 360^\circ \) and set up an equation using the given algebraic expressions for each angle. Solving this equation gives the required value of \( x \).

Name: ## Problem 15: Solve for \( x \).### Problem Statement:You are given
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: ## Problem 15: Solve for \( x \).### Problem Statement:You are given a quadrilateral with the internal angles defined algebraically. The four angles are denoted as follows:1. Top-left angle: \( (10x + 6)^\circ \)2. Bottom-left angle: \( (13x - 2)^\c