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 1: Find \( m \ 1 \).
### Description:
The image contains a triangle within a rectangle. Two angles of the triangle are labeled as \( 89.2^\circ \) and \( 48.5^\circ \). The third angle is labeled as \( m \ 1 \).
### Diagram Explanation:
- **Triangle**: A three-sided polygon with one angle measuring \( 89.2^\circ \), another measuring \( 48.5^\circ \), and the third angle to be calculated.
- **Rectangle**: The rectangular boundary around the triangle appears to simply frame it, with no additional relevant information given.
### Educational Objective:
Calculate the measure of angle \( m \ 1 \) in the triangle using the properties of interior angles in a triangle. The sum of interior angles in a triangle is always \( 180^\circ \).
### Solution Approach:
To find \( m \ 1 \):
1. Use the formula for the sum of angles in a triangle:
\[
m \ 1 = 180^\circ - (89.2^\circ + 48.5^\circ)
\]
2. Perform the calculation to find \( m \ 1 \).
This exercise helps reinforce the understanding of basic geometric principles and the calculation of unknown angles in triangles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70dd3339-9069-4b36-b997-58da94976e85%2F89bf9a73-1d68-43ec-98c1-c0af4dd672c6%2Fdym5p7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 1: Find \( m \ 1 \).
### Description:
The image contains a triangle within a rectangle. Two angles of the triangle are labeled as \( 89.2^\circ \) and \( 48.5^\circ \). The third angle is labeled as \( m \ 1 \).
### Diagram Explanation:
- **Triangle**: A three-sided polygon with one angle measuring \( 89.2^\circ \), another measuring \( 48.5^\circ \), and the third angle to be calculated.
- **Rectangle**: The rectangular boundary around the triangle appears to simply frame it, with no additional relevant information given.
### Educational Objective:
Calculate the measure of angle \( m \ 1 \) in the triangle using the properties of interior angles in a triangle. The sum of interior angles in a triangle is always \( 180^\circ \).
### Solution Approach:
To find \( m \ 1 \):
1. Use the formula for the sum of angles in a triangle:
\[
m \ 1 = 180^\circ - (89.2^\circ + 48.5^\circ)
\]
2. Perform the calculation to find \( m \ 1 \).
This exercise helps reinforce the understanding of basic geometric principles and the calculation of unknown angles in triangles.
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