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
Question
![**Problem: Calculation of Angles in a Triangle**
The measures of the angles of a triangle are shown in the figure below. Solve for \( x \).
**Diagram Explanation:**
The diagram depicts a triangle with its three angles labeled:
- The angle at the top-left corner is represented as \((x + 14)^\circ\).
- The angle at the bottom-right corner is labeled as \(42^\circ\).
- The angle at the bottom-left corner is labeled as \(108^\circ\).
**Solution Steps:**
1. Recall that the sum of the angles in any triangle is always \(180^\circ\).
2. Set up the equation based on the sum of the angles:
\[
(x + 14)^\circ + 42^\circ + 108^\circ = 180^\circ
\]
3. Simplify and solve the equation for \( x \):
\[
x + 14 + 42 + 108 = 180
\]
\[
x + 164 = 180
\]
\[
x = 180 - 164
\]
\[
x = 16
\]
Thus, the value of \( x \) is \( 16 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1ee66a4-8e77-4cb9-b1b9-9bd40d747386%2F5d442f76-e4aa-4d8c-887f-f1c03b73fb6f%2Fe83ew1_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Calculation of Angles in a Triangle**
The measures of the angles of a triangle are shown in the figure below. Solve for \( x \).
**Diagram Explanation:**
The diagram depicts a triangle with its three angles labeled:
- The angle at the top-left corner is represented as \((x + 14)^\circ\).
- The angle at the bottom-right corner is labeled as \(42^\circ\).
- The angle at the bottom-left corner is labeled as \(108^\circ\).
**Solution Steps:**
1. Recall that the sum of the angles in any triangle is always \(180^\circ\).
2. Set up the equation based on the sum of the angles:
\[
(x + 14)^\circ + 42^\circ + 108^\circ = 180^\circ
\]
3. Simplify and solve the equation for \( x \):
\[
x + 14 + 42 + 108 = 180
\]
\[
x + 164 = 180
\]
\[
x = 180 - 164
\]
\[
x = 16
\]
Thus, the value of \( x \) is \( 16 \).
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