**Problem Statement:** Find \( x \). **Diagram Explanation:** The image shows a right triangle with two angles labeled: 1. The right angle is implicit, pointing at the corner with a traditional right-angle square symbol. 2. One angle is labeled \((2x - 2)^\circ\). 3. The other angle is labeled \((x + 5)^\circ\). **Solution Steps:** In a right triangle, the sum of the angles is \(90^\circ + 90^\circ = 180^\circ\). Therefore: \[ 90^\circ + (2x - 2)^\circ + (x + 5)^\circ = 180^\circ \] To find \( x \), first combine the angle expressions: \[ (2x - 2) + (x + 5) = 90 \] \[ 2x - 2 + x + 5 = 90 \] Simplify and combine like terms: \[ 3x + 3 = 90 \] Subtract 3 from both sides: \[ 3x = 87 \] Divide by 3: \[ x = 29 \] Therefore, the value of \( x \) is \( 29 \). **Answer:** \( x = 29 \)
**Problem Statement:** Find \( x \). **Diagram Explanation:** The image shows a right triangle with two angles labeled: 1. The right angle is implicit, pointing at the corner with a traditional right-angle square symbol. 2. One angle is labeled \((2x - 2)^\circ\). 3. The other angle is labeled \((x + 5)^\circ\). **Solution Steps:** In a right triangle, the sum of the angles is \(90^\circ + 90^\circ = 180^\circ\). Therefore: \[ 90^\circ + (2x - 2)^\circ + (x + 5)^\circ = 180^\circ \] To find \( x \), first combine the angle expressions: \[ (2x - 2) + (x + 5) = 90 \] \[ 2x - 2 + x + 5 = 90 \] Simplify and combine like terms: \[ 3x + 3 = 90 \] Subtract 3 from both sides: \[ 3x = 87 \] Divide by 3: \[ x = 29 \] Therefore, the value of \( x \) is \( 29 \). **Answer:** \( x = 29 \)
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
Related questions
Question
![**Problem Statement:**
Find \( x \).
**Diagram Explanation:**
The image shows a right triangle with two angles labeled:
1. The right angle is implicit, pointing at the corner with a traditional right-angle square symbol.
2. One angle is labeled \((2x - 2)^\circ\).
3. The other angle is labeled \((x + 5)^\circ\).
**Solution Steps:**
In a right triangle, the sum of the angles is \(90^\circ + 90^\circ = 180^\circ\). Therefore:
\[
90^\circ + (2x - 2)^\circ + (x + 5)^\circ = 180^\circ
\]
To find \( x \), first combine the angle expressions:
\[
(2x - 2) + (x + 5) = 90
\]
\[
2x - 2 + x + 5 = 90
\]
Simplify and combine like terms:
\[
3x + 3 = 90
\]
Subtract 3 from both sides:
\[
3x = 87
\]
Divide by 3:
\[
x = 29
\]
Therefore, the value of \( x \) is \( 29 \).
**Answer:**
\( x = 29 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1932883-2c5b-49a7-9cf0-01e234752a0d%2F8630028e-7e7b-4729-be71-e306659b4ac6%2Fygydrie.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( x \).
**Diagram Explanation:**
The image shows a right triangle with two angles labeled:
1. The right angle is implicit, pointing at the corner with a traditional right-angle square symbol.
2. One angle is labeled \((2x - 2)^\circ\).
3. The other angle is labeled \((x + 5)^\circ\).
**Solution Steps:**
In a right triangle, the sum of the angles is \(90^\circ + 90^\circ = 180^\circ\). Therefore:
\[
90^\circ + (2x - 2)^\circ + (x + 5)^\circ = 180^\circ
\]
To find \( x \), first combine the angle expressions:
\[
(2x - 2) + (x + 5) = 90
\]
\[
2x - 2 + x + 5 = 90
\]
Simplify and combine like terms:
\[
3x + 3 = 90
\]
Subtract 3 from both sides:
\[
3x = 87
\]
Divide by 3:
\[
x = 29
\]
Therefore, the value of \( x \) is \( 29 \).
**Answer:**
\( x = 29 \)
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