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
Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![**Problem Statement:**
Given \( \triangle JKL \), find \( m\angle L \).
**Diagram Explanation:**
The diagram shows triangle \( JKL \) with:
- \( \angle J \) labeled as \( (2x + 7)^\circ \)
- \( \angle K \) labeled as \( (13x - 9)^\circ \)
- \( \angle L \) labeled as \( (4x + 11)^\circ \)
**Multiple-Choice Answers:**
- 68°
- 58°
- 29°
- 47°
To solve for \( m\angle L \), you need to use the triangle angle sum property, which states that the sum of the angles in a triangle is always 180°:
\[
(2x + 7) + (13x - 9) + (4x + 11) = 180
\]
Simplify and solve for \( x \):
\[
2x + 7 + 13x - 9 + 4x + 11 = 180
\]
\[
19x + 9 = 180
\]
\[
19x = 171
\]
\[
x = 9
\]
Now, substitute \( x = 9 \) back into \( \angle L \):
\[
m\angle L = 4x + 11 = 4(9) + 11 = 36 + 11 = 47^\circ
\]
Therefore, the correct answer is:
- 47°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7245aef9-c798-4f68-8116-7b90c3c18a0a%2F1ada65a8-b4cb-4d8b-84bb-130ca35f3a90%2Fzdquio8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given \( \triangle JKL \), find \( m\angle L \).
**Diagram Explanation:**
The diagram shows triangle \( JKL \) with:
- \( \angle J \) labeled as \( (2x + 7)^\circ \)
- \( \angle K \) labeled as \( (13x - 9)^\circ \)
- \( \angle L \) labeled as \( (4x + 11)^\circ \)
**Multiple-Choice Answers:**
- 68°
- 58°
- 29°
- 47°
To solve for \( m\angle L \), you need to use the triangle angle sum property, which states that the sum of the angles in a triangle is always 180°:
\[
(2x + 7) + (13x - 9) + (4x + 11) = 180
\]
Simplify and solve for \( x \):
\[
2x + 7 + 13x - 9 + 4x + 11 = 180
\]
\[
19x + 9 = 180
\]
\[
19x = 171
\]
\[
x = 9
\]
Now, substitute \( x = 9 \) back into \( \angle L \):
\[
m\angle L = 4x + 11 = 4(9) + 11 = 36 + 11 = 47^\circ
\]
Therefore, the correct answer is:
- 47°
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