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
The diagram shows a straight line LMN with a point Q above it, creating two angles: ∠LMQ and ∠NMQ.
**Questions:**
(a) **Identify the type of angle pair formed by ∠LMQ and ∠NMQ. Explain your reasoning.**
(b) **Given that m∠LMQ = 5x – 2 and m∠NMQ = 4x + 38, solve for x. Provide detailed calculations.**
**Solutions:**
*Answer:*
(a) *Discuss whether these angles are complementary, supplementary, or another type, based on their arrangement.*
(b) *Perform algebraic steps to find the value of x, showing your work.*
*Example Solution:*
- Since line MN is straight, angles ∠LMQ and ∠NMQ are supplementary, thus adding up to 180 degrees.
- Equation setup: (5x – 2) + (4x + 38) = 180
- Solve the equation to find x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3881924-b741-4ed0-b564-f01fa8337025%2F21e605f6-9b7c-4fb0-9d6c-36fcb2eeffb6%2F4kc05le_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instructions: Based on the provided figure, answer the following questions:**
1. Analyze the figure to respond to the questions.
The diagram shows a straight line LMN with a point Q above it, creating two angles: ∠LMQ and ∠NMQ.
**Questions:**
(a) **Identify the type of angle pair formed by ∠LMQ and ∠NMQ. Explain your reasoning.**
(b) **Given that m∠LMQ = 5x – 2 and m∠NMQ = 4x + 38, solve for x. Provide detailed calculations.**
**Solutions:**
*Answer:*
(a) *Discuss whether these angles are complementary, supplementary, or another type, based on their arrangement.*
(b) *Perform algebraic steps to find the value of x, showing your work.*
*Example Solution:*
- Since line MN is straight, angles ∠LMQ and ∠NMQ are supplementary, thus adding up to 180 degrees.
- Equation setup: (5x – 2) + (4x + 38) = 180
- Solve the equation to find x.
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