(8x) W FIND X. (21x 12) (10x + 9)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Title: 9.1 Mastery: Central Angles & Arcs**
**Objective:**
Find the value of \( x \).
**Description:**
The diagram is of a circle with center \( Z \). Three central angles are shown in the circle, each with their respective measures given in terms of \( x \).
**Details of the Diagram:**
- The central angle \( \angle VZW \) is marked as \( (8x)^\circ \).
- The central angle \( \angle YZR \) is marked as \( (10x + 9)^\circ \).
- The central angle \( \angle WZY \) is marked as \( (21x - 12)^\circ \).
Since the sum of the angles surrounding a point (such as the center of a circle) is always \( 360^\circ \), you can set up the following equation to solve for \( x \):
\[ (8x) + (10x + 9) + (21x - 12) = 360 \]
**Solution Steps:**
1. Combine like terms:
\[ 8x + 10x + 21x + 9 - 12 = 360 \]
\[ 39x - 3 = 360 \]
2. Add 3 to both sides:
\[ 39x = 363 \]
3. Divide both sides by 39:
\[ x = \frac{363}{39} \]
\[ x = 9.31 \]
**Answer:**
\[ x = 9.31 \]
You can check the solution by substituting \( x \) back into each angle measure to verify their sum is \( 360^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34dbf93a-185c-4522-bbbf-f73f18b87311%2F8b9907d5-53be-4965-b791-3c555c8b354a%2Fyxkt47_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: 9.1 Mastery: Central Angles & Arcs**
**Objective:**
Find the value of \( x \).
**Description:**
The diagram is of a circle with center \( Z \). Three central angles are shown in the circle, each with their respective measures given in terms of \( x \).
**Details of the Diagram:**
- The central angle \( \angle VZW \) is marked as \( (8x)^\circ \).
- The central angle \( \angle YZR \) is marked as \( (10x + 9)^\circ \).
- The central angle \( \angle WZY \) is marked as \( (21x - 12)^\circ \).
Since the sum of the angles surrounding a point (such as the center of a circle) is always \( 360^\circ \), you can set up the following equation to solve for \( x \):
\[ (8x) + (10x + 9) + (21x - 12) = 360 \]
**Solution Steps:**
1. Combine like terms:
\[ 8x + 10x + 21x + 9 - 12 = 360 \]
\[ 39x - 3 = 360 \]
2. Add 3 to both sides:
\[ 39x = 363 \]
3. Divide both sides by 39:
\[ x = \frac{363}{39} \]
\[ x = 9.31 \]
**Answer:**
\[ x = 9.31 \]
You can check the solution by substituting \( x \) back into each angle measure to verify their sum is \( 360^\circ \).
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