I just need my answer checked and /or edited. ## Transcription and Explanation of the Diagram in the Given Geometry Problem### Problem StatementIn the diagram below of triangle $ \triangle ABC $, side $ BC $ is extended to point $ D $. The measures of the angles are given as follows:- $ m \angle A = 3x + 2 $- $ m \angle LB = 4x - 1 $- $ m \angle ACD = x + 19 $Find $ m \angle LB $.### Diagram DescriptionThe diagram shows an extended triangle with the following details:- Point $ A $, $ B $, $ C $, and $ D $ are labeled with lines connecting them to form the structure of the triangle and the extended line.- Angle measures are marked on the diagram as follows: - $ \angle A = 3x + 2 $ - The external angle $ \angle ACD = x + 19 $ - The angle $ \angle LB = 4x - 1 $### Solution Steps1. **Equate the Angles**: The exterior angle $ ACD $ of triangle $ ABC $ is equal to the sum of the opposite interior angles $ A $ and $ B $: \[ A + B = ACD \] \[ 3x + 2 + (4x - 1) = x + 19 \]2. **Simplify the Equation**: \[ 5x + 1 = x + 19 \]3. **Solve for $ x $**: \[ 5x - x = 19 - 1 \] \[ 4x = 18 \] \[ x = \frac{18}{4} = 4.5 \]4. **Find $ m \angle LB $**: Substitute $ x = 4.5 $ into $ 4x - 1 $: \[ m \angle LB = 4(4.5) - 1 = 18 - 1 = 17 \]### ConclusionThe measure of $ m \angle LB $ is $ 17 $ degrees. This problem illustrates the relationship between interior and exterior angles in geometry, highlighting

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Description: I just need my answer checked and /or edited. ## Transcription and Explanation of the Diagram in the Given Geometry Problem### Problem StatementIn the diagram below of triangle $ \triangle ABC $, side $ BC $ is extended to point $ D $. The meas

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Answered: n the diagram below of AABC, side BC is…

Math

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n the diagram below of AABC, side BC is extended to point D, mLA = 3x + 2, mLB = 4x-1, ACD = x+19. Find mLB. %3D A 3x+2 A+b =ACD x+2 + 2x+15 =X+19 X+19 4x D 5xジ=xt19 -17 5xニメ+2 ーx -× X=2

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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I just need my answer checked and /or edited.

## Transcription and Explanation of the Diagram in the Given Geometry Problem

### Problem Statement

In the diagram below of triangle $ \triangle ABC $, side $ BC $ is extended to point $ D $. The measures of the angles are given as follows:
- $ m \angle A = 3x + 2 $
- $ m \angle LB = 4x - 1 $
- $ m \angle ACD = x + 19 $

Find $ m \angle LB $.

### Diagram Description

The diagram shows an extended triangle with the following details:

- Point $ A $, $ B $, $ C $, and $ D $ are labeled with lines connecting them to form the structure of the triangle and the extended line.
- Angle measures are marked on the diagram as follows:
- $ \angle A = 3x + 2 $
- The external angle $ \angle ACD = x + 19 $
- The angle $ \angle LB = 4x - 1 $

### Solution Steps

1. **Equate the Angles**:
The exterior angle $ ACD $ of triangle $ ABC $ is equal to the sum of the opposite interior angles $ A $ and $ B $:
\[
A + B = ACD
\]
\[
3x + 2 + (4x - 1) = x + 19
\]

2. **Simplify the Equation**:
\[
5x + 1 = x + 19
\]

3. **Solve for $ x $**:
\[
5x - x = 19 - 1
\]
\[
4x = 18
\]
\[
x = \frac{18}{4} = 4.5
\]

4. **Find $ m \angle LB $**:
Substitute $ x = 4.5 $ into $ 4x - 1 $:
\[
m \angle LB = 4(4.5) - 1 = 18 - 1 = 17
\]

### Conclusion

The measure of $ m \angle LB $ is $ 17 $ degrees.

This problem illustrates the relationship between interior and exterior angles in geometry, highlighting

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