Solve for x in each figure and order the figures according to their values of x , from least to greatest. B 90° (2x+8) 90 (2x + 8)° 100 (5x)° (5x) Y 150 60° B. (6x) (5x + 25)° E 60° 150
Solve for x in each figure and order the figures according to their values of x , from least to greatest. B 90° (2x+8) 90 (2x + 8)° 100 (5x)° (5x) Y 150 60° B. (6x) (5x + 25)° E 60° 150
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Solving for x in Geometric Figures**
In this exercise, you will solve for the variable \( x \) in different geometric figures and order the figures according to their values of \( x \), from least to greatest.
---
### Figure 1: Quadrilateral \(ABCD\)
This is a rectangle with the following angles:
- \( \angle A = 90^\circ \)
- \( \angle B = 90^\circ \)
- \( \angle C = (2x + 8)^\circ \)
- \( \angle D = (2x + 8)^\circ \)
**Equations:**
Since the sum of interior angles in a rectangle is always \(360^\circ\), we have:
\[ 90^\circ + 90^\circ + (2x + 8)^\circ + (2x + 8)^\circ = 360^\circ \]
Simplifying the equation:
\[ 180 + 4x + 16 = 360 \]
\[ 4x + 196 = 360 \]
\[ 4x = 244 \]
\[ x = 61 \]
---
### Figure 2: Triangle \(XYZ\)
This is a triangle with the following angles:
- \( \angle X = 100^\circ \)
- \( \angle Z = (5x)^\circ \)
- \( \angle Y = (5x)^\circ \)
**Equations:**
Since the sum of interior angles in a triangle is always \(180^\circ\), we have:
\[ 100^\circ + (5x) + (5x) = 180^\circ \]
Simplifying the equation:
\[ 100 + 10x = 180 \]
\[ 10x = 80 \]
\[ x = 8 \]
---
### Figure 3: Hexagon \(ABCDEF\)
This is a hexagon with the following angles:
- \( \angle A = 60^\circ \)
- \( \angle B = (6x)^\circ \)
- \( \angle C = 150^\circ \)
- \( \angle D = 60^\circ \)
- \( \angle E = (5x + 25)^\circ \)
- \( \angle F = 150^\circ \)
**Equations:**
Since the sum of interior angles in a hexagon is always \((6-2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F607cced0-c3e1-4338-aeaf-f61d5cbda073%2F98db7534-1529-4545-93ca-44b1ab96dacd%2F5d6t0nc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving for x in Geometric Figures**
In this exercise, you will solve for the variable \( x \) in different geometric figures and order the figures according to their values of \( x \), from least to greatest.
---
### Figure 1: Quadrilateral \(ABCD\)
This is a rectangle with the following angles:
- \( \angle A = 90^\circ \)
- \( \angle B = 90^\circ \)
- \( \angle C = (2x + 8)^\circ \)
- \( \angle D = (2x + 8)^\circ \)
**Equations:**
Since the sum of interior angles in a rectangle is always \(360^\circ\), we have:
\[ 90^\circ + 90^\circ + (2x + 8)^\circ + (2x + 8)^\circ = 360^\circ \]
Simplifying the equation:
\[ 180 + 4x + 16 = 360 \]
\[ 4x + 196 = 360 \]
\[ 4x = 244 \]
\[ x = 61 \]
---
### Figure 2: Triangle \(XYZ\)
This is a triangle with the following angles:
- \( \angle X = 100^\circ \)
- \( \angle Z = (5x)^\circ \)
- \( \angle Y = (5x)^\circ \)
**Equations:**
Since the sum of interior angles in a triangle is always \(180^\circ\), we have:
\[ 100^\circ + (5x) + (5x) = 180^\circ \]
Simplifying the equation:
\[ 100 + 10x = 180 \]
\[ 10x = 80 \]
\[ x = 8 \]
---
### Figure 3: Hexagon \(ABCDEF\)
This is a hexagon with the following angles:
- \( \angle A = 60^\circ \)
- \( \angle B = (6x)^\circ \)
- \( \angle C = 150^\circ \)
- \( \angle D = 60^\circ \)
- \( \angle E = (5x + 25)^\circ \)
- \( \angle F = 150^\circ \)
**Equations:**
Since the sum of interior angles in a hexagon is always \((6-2
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