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(a) What type of angle pair are

(a) What type of angle pair are

Elementary Geometry For College Students, 7e
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
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**Instructions: Based on the provided figure, answer the following questions:** 1. Analyze the figure to respond to the questions. ![Diagram](placeholder-image-url) 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.
Transcribed Image Text:**Instructions: Based on the provided figure, answer the following questions:** 1. Analyze the figure to respond to the questions. ![Diagram](placeholder-image-url) 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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