## 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.

Answered: 1. Find m 1. 89.2 48.5

Math

Geometry

1. Find m 1. 89.2 48.5

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

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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.

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