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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![### Rhombus Problem - Finding Angle Measure
The figure below is a Rhombus.
**Problem Statement:**
Find the measure of ∠HGI.
**Diagram Description:**
The diagram depicts rhombus FGHI with diagonals intersecting at point J. The angle at vertex F is labeled as (7x - 1)°, and the angle at vertex H is labeled as (4x + 3)°.
#### Diagram:
```
F
/\
/ \
G /____\ H
\ /
\/
J
```
- **FGHI** is a rhombus with diagonals intersecting at \( J \).
- \( \angle F \): \( (7x - 1)° \)
- \( \angle H \): \( (4x + 3)° \)
#### Instructions:
Make sure you plug \( x \) back in to get the correct answer.
**To Find:**
\[ m\angle HGI = \]
Feel free to solve the problem using the properties of rhombuses and linear equations as required.
### Key Properties of Rhombuses:
1. All sides are of equal length.
2. Opposite angles are equal.
3. Diagonals bisect each other at right angles (90°).
This information is crucial in determining the value of \( x \) and subsequently the required angle.
[type your answer in the box provided]
**\( m\angle HGI = \)** \( \_\_\_\_\_ \)
Hope this helps you in understanding how to determine specific angle measures in geometrical figures!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32fdead-cf8a-44ab-a7f8-9f10e201d4c1%2Fe73884cb-444e-450c-af40-63ffa841fefb%2Frtxi3x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Rhombus Problem - Finding Angle Measure
The figure below is a Rhombus.
**Problem Statement:**
Find the measure of ∠HGI.
**Diagram Description:**
The diagram depicts rhombus FGHI with diagonals intersecting at point J. The angle at vertex F is labeled as (7x - 1)°, and the angle at vertex H is labeled as (4x + 3)°.
#### Diagram:
```
F
/\
/ \
G /____\ H
\ /
\/
J
```
- **FGHI** is a rhombus with diagonals intersecting at \( J \).
- \( \angle F \): \( (7x - 1)° \)
- \( \angle H \): \( (4x + 3)° \)
#### Instructions:
Make sure you plug \( x \) back in to get the correct answer.
**To Find:**
\[ m\angle HGI = \]
Feel free to solve the problem using the properties of rhombuses and linear equations as required.
### Key Properties of Rhombuses:
1. All sides are of equal length.
2. Opposite angles are equal.
3. Diagonals bisect each other at right angles (90°).
This information is crucial in determining the value of \( x \) and subsequently the required angle.
[type your answer in the box provided]
**\( m\angle HGI = \)** \( \_\_\_\_\_ \)
Hope this helps you in understanding how to determine specific angle measures in geometrical figures!
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