+ 4)° and E = (29x – 6)°, find the measures A/B C/D m E F G/H n xact answers.
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°.
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![**Problem Statement:**
Given:
- \( C = (23x + 4)^\circ \)
- \( E = (29x - 6)^\circ \)
Find the measures of \( C \) and \( E \).
**Diagram Explanation:**
The diagram shows two parallel lines, \( m \parallel n \), intersected by a transversal.
- Line \( m \) is indicated with points A, B, C, D in a sequence.
- Line \( n \) is indicated with points E, F, G, H in a sequence.
- The transversal creates angle C at the intersection with line \( m \) and angle E at the intersection with line \( n \).
**Solution Steps:**
To find the measures of \( C \) and \( E \), set up an equation using the properties of parallel lines and the fact that \( C \) and \( E \) are alternate interior angles, making them equal:
\[ (23x + 4) = (29x - 6) \]
Solve for \( x \) and substitute back to find the exact angle measures.
**Answer Input:**
Enter the exact answers:
- \( C = \) [Enter value] °
- \( E = \) [Enter value] °](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb8f64bb-a739-44c8-9c71-41ea58cbca19%2F629535e1-7648-4136-b71a-717eb5dedd58%2F5tk1dir_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given:
- \( C = (23x + 4)^\circ \)
- \( E = (29x - 6)^\circ \)
Find the measures of \( C \) and \( E \).
**Diagram Explanation:**
The diagram shows two parallel lines, \( m \parallel n \), intersected by a transversal.
- Line \( m \) is indicated with points A, B, C, D in a sequence.
- Line \( n \) is indicated with points E, F, G, H in a sequence.
- The transversal creates angle C at the intersection with line \( m \) and angle E at the intersection with line \( n \).
**Solution Steps:**
To find the measures of \( C \) and \( E \), set up an equation using the properties of parallel lines and the fact that \( C \) and \( E \) are alternate interior angles, making them equal:
\[ (23x + 4) = (29x - 6) \]
Solve for \( x \) and substitute back to find the exact angle measures.
**Answer Input:**
Enter the exact answers:
- \( C = \) [Enter value] °
- \( E = \) [Enter value] °
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