Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.2: The Rectangular Coordinate System
Problem 92PS: Draw an angle in standard position whose terminal side contains the point (2, –3). Find the...
Related questions
Question
![**Problem Statement:**
In the triangle below, suppose that \( m \angle J = (5x - 8)^\circ \), \( m \angle K = (2x + 4)^\circ \), and \( m \angle L = x^\circ \).
Find the degree measure of each angle in the triangle.
**Diagram:**
A triangle \( \triangle JKL \) is shown with its angles marked as follows:
- \( \angle J \) is marked as \( (5x - 8)^\circ \)
- \( \angle K \) is marked as \( (2x + 4)^\circ \)
- \( \angle L \) is marked as \( x^\circ \)
There is also a boxed section for answers to be filled in, which includes:
- \( m \angle J = \) _____ \(^\circ \)
- \( m \angle K = \) _____ \(^\circ \)
- \( m \angle L = \) _____ \(^\circ \)
**Solution Steps:**
1. **Sum of Angles in a Triangle:**
The sum of the interior angles in any triangle is \( 180^\circ \). Therefore, we can set up the following equation:
\[
m \angle J + m \angle K + m \angle L = 180^\circ
\]
Substituting the given expressions for \( m \angle J \), \( m \angle K \), and \( m \angle L \):
\[
(5x - 8) + (2x + 4) + x = 180
\]
2. **Combine Like Terms:**
Combine the terms involving \( x \) and the constant terms:
\[
5x + 2x + x - 8 + 4 = 180
\]
\[
8x - 4 = 180
\]
3. **Solve for \( x \):**
Add 4 to both sides of the equation:
\[
8x - 4 + 4 = 180 + 4
\]
\[
8x = 184
\]
Divide both sides by 8:
\[
x = \frac{184}{8}
\]
\[
x = 23
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09f203f0-592a-44e7-b68f-d36235de84a7%2Fa6f90976-3cd9-462a-a9c4-10c114a56467%2Faprtkhv.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In the triangle below, suppose that \( m \angle J = (5x - 8)^\circ \), \( m \angle K = (2x + 4)^\circ \), and \( m \angle L = x^\circ \).
Find the degree measure of each angle in the triangle.
**Diagram:**
A triangle \( \triangle JKL \) is shown with its angles marked as follows:
- \( \angle J \) is marked as \( (5x - 8)^\circ \)
- \( \angle K \) is marked as \( (2x + 4)^\circ \)
- \( \angle L \) is marked as \( x^\circ \)
There is also a boxed section for answers to be filled in, which includes:
- \( m \angle J = \) _____ \(^\circ \)
- \( m \angle K = \) _____ \(^\circ \)
- \( m \angle L = \) _____ \(^\circ \)
**Solution Steps:**
1. **Sum of Angles in a Triangle:**
The sum of the interior angles in any triangle is \( 180^\circ \). Therefore, we can set up the following equation:
\[
m \angle J + m \angle K + m \angle L = 180^\circ
\]
Substituting the given expressions for \( m \angle J \), \( m \angle K \), and \( m \angle L \):
\[
(5x - 8) + (2x + 4) + x = 180
\]
2. **Combine Like Terms:**
Combine the terms involving \( x \) and the constant terms:
\[
5x + 2x + x - 8 + 4 = 180
\]
\[
8x - 4 = 180
\]
3. **Solve for \( x \):**
Add 4 to both sides of the equation:
\[
8x - 4 + 4 = 180 + 4
\]
\[
8x = 184
\]
Divide both sides by 8:
\[
x = \frac{184}{8}
\]
\[
x = 23
\
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL