Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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![### Educational Problem: Finding the Value of \( x \)
**Question:**
What is the value of \( x \)?
**Diagram Description:**
- There is a circle with points \( S \), \( U \), and \( T \) on its circumference.
- Three radii of the circle originate from point \( V \) at the center of the circle and extend to points \( S \), \( U \), and \( T \).
- The angle \( \angle SVU = x + 78^\circ \).
- The angle \( \angle SVT = 71^\circ \).
- The angle \( \angle TVU = x + 77^\circ \).
**Formula for Interior Angles in a Circle:**
In a circle, the sum of interior angles at the center of the circle should be \( 360^\circ \).
Given angles:
\[ \angle SVU + \angle SVT + \angle TVU = 360^\circ \]
Substitute the given angles:
\[ (x + 78^\circ) + 71^\circ + (x + 77^\circ) = 360^\circ \]
**Equation Setup:**
Combine like terms and solve for \( x \):
\[ x + 78^\circ + 71^\circ + x + 77^\circ = 360^\circ \]
\[ 2x + 226^\circ = 360^\circ \]
\[ 2x = 360^\circ - 226^\circ \]
\[ 2x = 134^\circ \]
\[ x = 67^\circ \]
**Answer:**
\[ x = 67^\circ \]
Use the input box to enter your answer: \( x = \boxed{67^\circ} \)](https://content.bartleby.com/qna-images/question/5f6754e4-b4a1-4709-8cf0-90421fcab68c/3e7b132d-b5bf-439c-a2a7-a3d7d032d51c/587h3ak_processed.jpeg)
Transcribed Image Text:### Educational Problem: Finding the Value of \( x \)
**Question:**
What is the value of \( x \)?
**Diagram Description:**
- There is a circle with points \( S \), \( U \), and \( T \) on its circumference.
- Three radii of the circle originate from point \( V \) at the center of the circle and extend to points \( S \), \( U \), and \( T \).
- The angle \( \angle SVU = x + 78^\circ \).
- The angle \( \angle SVT = 71^\circ \).
- The angle \( \angle TVU = x + 77^\circ \).
**Formula for Interior Angles in a Circle:**
In a circle, the sum of interior angles at the center of the circle should be \( 360^\circ \).
Given angles:
\[ \angle SVU + \angle SVT + \angle TVU = 360^\circ \]
Substitute the given angles:
\[ (x + 78^\circ) + 71^\circ + (x + 77^\circ) = 360^\circ \]
**Equation Setup:**
Combine like terms and solve for \( x \):
\[ x + 78^\circ + 71^\circ + x + 77^\circ = 360^\circ \]
\[ 2x + 226^\circ = 360^\circ \]
\[ 2x = 360^\circ - 226^\circ \]
\[ 2x = 134^\circ \]
\[ x = 67^\circ \]
**Answer:**
\[ x = 67^\circ \]
Use the input box to enter your answer: \( x = \boxed{67^\circ} \)
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