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 the value of \( x \).
*Diagram Explanation:*
1. The diagram shows a right angle (90°) with a smaller triangle inscribed at its vertex.
2. There are three angles mentioned in the diagram:
- One angle measures 49°.
- Another angle is depicted as an unknown angle but expressed in terms of \( x \) as \( (3x + 5)° \).
- The right angle measures 90°.
To solve for \( x \):
Given that the sum of the angles in any triangle is always 180°, we can set up the following equation based on the provided angles:
\[ 49° + (3x + 5)° + 90° = 180° \]
Simplifying the equation:
\[ 49 + 3x + 5 + 90 = 180 \]
\[ 144 + 3x = 180 \]
Subtract 144 from both sides:
\[ 3x = 36 \]
Divide by 3:
\[ x = 12 \]
Thus, the value of \( x \) is \( 12 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e449208-cf4f-4e53-8cac-e5c4c8cafa96%2F8a9b509d-ab64-4986-afc4-1159189fd2b1%2Fxz4evi7_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the value of \( x \).
*Diagram Explanation:*
1. The diagram shows a right angle (90°) with a smaller triangle inscribed at its vertex.
2. There are three angles mentioned in the diagram:
- One angle measures 49°.
- Another angle is depicted as an unknown angle but expressed in terms of \( x \) as \( (3x + 5)° \).
- The right angle measures 90°.
To solve for \( x \):
Given that the sum of the angles in any triangle is always 180°, we can set up the following equation based on the provided angles:
\[ 49° + (3x + 5)° + 90° = 180° \]
Simplifying the equation:
\[ 49 + 3x + 5 + 90 = 180 \]
\[ 144 + 3x = 180 \]
Subtract 144 from both sides:
\[ 3x = 36 \]
Divide by 3:
\[ x = 12 \]
Thus, the value of \( x \) is \( 12 \).
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