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 Statement:**
Find the value of each variable in the figure on the right.
**Diagram Description:**
The diagram shows a right triangle with angles labeled as follows:
- One angle measures \(32^\circ\).
- Another angle measures \(75^\circ\).
- The third angle is labeled as \(x^\circ\).
Additionally, there is a line with an angle marked as \(y^\circ\) adjacent to the triangle and continuing in a straight path, indicating that it is supplementary to angle \(x\).
**Solution:**
To solve for \(x\), note that the sum of angles in a triangle is \(180^\circ\). Therefore, calculate \(x\) as follows:
\[ x = 180^\circ - (32^\circ + 75^\circ) \]
Next, observe that the angle \(y\) is supplementary to \(x\) (they form a straight line), so:
\[ y = 180^\circ - x \]
**Answer Box:**
x = [__] (Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43eb41af-d84b-40c1-ba80-6ea778a40d08%2Fc1bb1441-8a3e-4b59-ab1f-e0ac6ec618a1%2Fca0ql3s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the value of each variable in the figure on the right.
**Diagram Description:**
The diagram shows a right triangle with angles labeled as follows:
- One angle measures \(32^\circ\).
- Another angle measures \(75^\circ\).
- The third angle is labeled as \(x^\circ\).
Additionally, there is a line with an angle marked as \(y^\circ\) adjacent to the triangle and continuing in a straight path, indicating that it is supplementary to angle \(x\).
**Solution:**
To solve for \(x\), note that the sum of angles in a triangle is \(180^\circ\). Therefore, calculate \(x\) as follows:
\[ x = 180^\circ - (32^\circ + 75^\circ) \]
Next, observe that the angle \(y\) is supplementary to \(x\) (they form a straight line), so:
\[ y = 180^\circ - x \]
**Answer Box:**
x = [__] (Simplify your answer.)
![For the figure shown on the right, find \( m \angle 1 \).
The image depicts a triangle with angles labeled as \( 61^\circ \) and \( 55^\circ \), and a side labeled with the number 1. An arrow points towards this side, indicating it as a reference for \( \angle 1 \).
Below the diagram, there is a prompt:
\( m \angle 1 = \) [ ]
To find \( m \angle 1 \), use the triangle angle sum property, which states that the sum of the interior angles of a triangle is always \( 180^\circ \).
Thus, calculate \( m \angle 1 = 180^\circ - 61^\circ - 55^\circ \).
This educational problem encourages understanding of basic geometry concepts related to triangle angle sums.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43eb41af-d84b-40c1-ba80-6ea778a40d08%2Fc1bb1441-8a3e-4b59-ab1f-e0ac6ec618a1%2F7tqgxrl_processed.png&w=3840&q=75)
Transcribed Image Text:For the figure shown on the right, find \( m \angle 1 \).
The image depicts a triangle with angles labeled as \( 61^\circ \) and \( 55^\circ \), and a side labeled with the number 1. An arrow points towards this side, indicating it as a reference for \( \angle 1 \).
Below the diagram, there is a prompt:
\( m \angle 1 = \) [ ]
To find \( m \angle 1 \), use the triangle angle sum property, which states that the sum of the interior angles of a triangle is always \( 180^\circ \).
Thus, calculate \( m \angle 1 = 180^\circ - 61^\circ - 55^\circ \).
This educational problem encourages understanding of basic geometry concepts related to triangle angle sums.
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