Homework Help is Here – Start Your Trial Now!
Math
Geometry
9. GIVEN: [1 and 0 2 are a linear pair. PROVE: m1 = 180° – m|2 Statements Reasons 1. Given 2. The angles in a linear pair are 1. 2. supplementary angles. 3. |4. Subtraction Property of Equality 3. mol+ m2 - 180° 4.

9. GIVEN: [1 and 0 2 are a linear pair. PROVE: m1 = 180° – m|2 Statements Reasons 1. Given 2. The angles in a linear pair are 1. 2. supplementary angles. 3. |4. Subtraction Property of Equality 3. mol+ m2 - 180° 4.

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
See similar textbooks
icon
Related questions
Question
100%

How to solve the equation and write a reason for each step

**Title: Proof of Angles in a Linear Pair** **Given:** ∠1 and ∠2 are a linear pair. **Objective:** Prove that \( m∠1 = 180° - m∠2 \). ### Diagram Explanation: The diagram illustrates two adjacent angles, ∠1 and ∠2, which form a straight line, indicating they are a linear pair. ### Proof Structure: | **Statements** | **Reasons** | |----------------------------------|-----------------------------------------------| | 1. ∠1 and ∠2 are a linear pair. | 1. Given | | 2. _?_ | 2. The angles in a linear pair are supplementary angles. | | 3. \( m∠1 + m∠2 = 180° \) | 3. _?_ | | 4. \( m∠1 = 180° - m∠2 \) | 4. Subtraction Property of Equality | ### Explanation of the Proof: 1. **Statement 1:** It's established that ∠1 and ∠2 are a linear pair as given in the problem outlines. 2. **Reason 2:** It states that angles in a linear pair are always supplementary, which means their measures add up to 180°. 3. **Statement 3:** Formally expresses the supplementary relationship as \( m∠1 + m∠2 = 180° \). 4. **Reason 4:** By applying the Subtraction Property of Equality, we derive that \( m∠1 = 180° - m∠2 \). This proof demonstrates the property that in a linear pair, the measure of one angle is equal to the difference between 180° and the measure of the other angle.
Transcribed Image Text:**Title: Proof of Angles in a Linear Pair** **Given:** ∠1 and ∠2 are a linear pair. **Objective:** Prove that \( m∠1 = 180° - m∠2 \). ### Diagram Explanation: The diagram illustrates two adjacent angles, ∠1 and ∠2, which form a straight line, indicating they are a linear pair. ### Proof Structure: | **Statements** | **Reasons** | |----------------------------------|-----------------------------------------------| | 1. ∠1 and ∠2 are a linear pair. | 1. Given | | 2. _?_ | 2. The angles in a linear pair are supplementary angles. | | 3. \( m∠1 + m∠2 = 180° \) | 3. _?_ | | 4. \( m∠1 = 180° - m∠2 \) | 4. Subtraction Property of Equality | ### Explanation of the Proof: 1. **Statement 1:** It's established that ∠1 and ∠2 are a linear pair as given in the problem outlines. 2. **Reason 2:** It states that angles in a linear pair are always supplementary, which means their measures add up to 180°. 3. **Statement 3:** Formally expresses the supplementary relationship as \( m∠1 + m∠2 = 180° \). 4. **Reason 4:** By applying the Subtraction Property of Equality, we derive that \( m∠1 = 180° - m∠2 \). This proof demonstrates the property that in a linear pair, the measure of one angle is equal to the difference between 180° and the measure of the other angle.
Expert Solution
Step 1

Proof in below

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer