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
Need this asap !
#### Solution Explanation:
To find \(m \angle TEP\), we will use the fact that the sum of angles in a triangle is always \(180^\circ\).
Given:
- \(\angle SEP = 90^\circ\) (right angle)
- \(\angle SET = 30^\circ 27' 40''\)
Steps:
1. Recall that in triangle SET, the sum of the angles is \(180^\circ\).
2. Since \(\angle SEP\) is a right angle, by definition it equals \(90^\circ\).
3. Determine \(m \angle TEP\) using the equation:
\[
\angle SEP + \angle SET + \angle TEP = 180^\circ
\]
Substituting in the known values:
\[
90^\circ + 30^\circ 27' 40'' + \angle TEP = 180^\circ
\]
\[
120^\circ 27' 40'' + \angle TEP = 180^\circ
\]
4. To find \(\angle TEP\), subtract \(120^\circ 27' 40''\) from \(180^\circ\):
\[
\angle TEP = 180^\circ - 120^\circ 27' 40''
\]
The remaining angle \(m \angle TEP\) calculates as:
\[
\angle TEP = 180^\circ - 120^\circ 27' 40'' = 59^\circ 32' 20''
\]
Thus, \(m \angle TEP = 59^\circ 32' 20''\).
#### Diagram Description:
The provided diagram consists of three points \(S\), \(T\), and \(P\) forming a triangle with point \(E\) at the vertex of the right angle (\(90^\circ\)). Point \(E\) forms two distinct angles, one being a right angle with \(S\) and \(P\) and another \(30^\circ 27' 40''\) with \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d94fb0e-3cb9-42c0-8e4a-cf5f8f1ded5d%2F88f12c2c-2f5b-488e-a482-96cbcec6f6e0%2F7ueazqh_processed.png&w=3840&q=75)
Transcribed Image Text:### Geometry Problem
#### Problem Statement:
In the diagram, \(\angle SEP\) is a right angle \(\angle SET = 30^\circ 27' 40''\). Find \(m \angle TEP\).
#### Solution Explanation:
To find \(m \angle TEP\), we will use the fact that the sum of angles in a triangle is always \(180^\circ\).
Given:
- \(\angle SEP = 90^\circ\) (right angle)
- \(\angle SET = 30^\circ 27' 40''\)
Steps:
1. Recall that in triangle SET, the sum of the angles is \(180^\circ\).
2. Since \(\angle SEP\) is a right angle, by definition it equals \(90^\circ\).
3. Determine \(m \angle TEP\) using the equation:
\[
\angle SEP + \angle SET + \angle TEP = 180^\circ
\]
Substituting in the known values:
\[
90^\circ + 30^\circ 27' 40'' + \angle TEP = 180^\circ
\]
\[
120^\circ 27' 40'' + \angle TEP = 180^\circ
\]
4. To find \(\angle TEP\), subtract \(120^\circ 27' 40''\) from \(180^\circ\):
\[
\angle TEP = 180^\circ - 120^\circ 27' 40''
\]
The remaining angle \(m \angle TEP\) calculates as:
\[
\angle TEP = 180^\circ - 120^\circ 27' 40'' = 59^\circ 32' 20''
\]
Thus, \(m \angle TEP = 59^\circ 32' 20''\).
#### Diagram Description:
The provided diagram consists of three points \(S\), \(T\), and \(P\) forming a triangle with point \(E\) at the vertex of the right angle (\(90^\circ\)). Point \(E\) forms two distinct angles, one being a right angle with \(S\) and \(P\) and another \(30^\circ 27' 40''\) with \(
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
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning