Find the measure of the numbered angles in the rhombus. The diagram Is not to scale. 44° 21 O m21 = 90, m22=44, and mZ3 = 46 O mZ1 = 90, mZ2=D46, and mZ3 = 44 O m21 = 90, mZ2=44, and mZ3 = 44 O m21 = 90, mZ2=44, and mZ3 = 68
Find the measure of the numbered angles in the rhombus. The diagram Is not to scale. 44° 21 O m21 = 90, m22=44, and mZ3 = 46 O mZ1 = 90, mZ2=D46, and mZ3 = 44 O m21 = 90, mZ2=44, and mZ3 = 44 O m21 = 90, mZ2=44, and mZ3 = 68
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
In the given diagram, the rhombus is divided into four smaller triangles. The diagram includes the following angles and sides:
- Angle at the top (marked as 44°)
- Four internal angles to be determined (labeled as 1, 2, and 3)
#### Potential Answers:
- **Option A:** \(m∠1 = 90°, \, m∠2 = 44°, \, \text{and} \, m∠3 = 46°\)
- **Option B:** \(m∠1 = 90°, \, m∠2 = 46°, \, \text{and} \, m∠3 = 44°\)
- **Option C:** \(m∠1 = 90°, \, m∠2 = 44°, \, \text{and} \, m∠3 = 44°\)
- **Option D:** \(m∠1 = 90°, \, m∠2 = 44°, \, \text{and} \, m∠3 = 68°\)
### Explanation:
To find the correct measures of the angles labeled 1, 2, and 3 in the rhombus, consider the properties of rhombuses, such as opposite angles being equal and the diagonals bisecting each other at right angles.
#### Additional Notes:
- **Diagram Specifics:** The diagram shows a rhombus with a specific angle of 44° at the top vertex, and the diagonals intersect forming four smaller triangles within the rhombus.
- **Required Knowledge:** Understanding of the properties of rhombuses and how diagonals intersect can help solve this problem correctly.
This problem is a typical example in geometry that tests understanding of angle relationships in quadrilaterals, particularly rhombuses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe59874f9-f705-461a-94a3-07d771601ab4%2Fc0c3d934-c9ac-4661-a878-3453938e5151%2F3k9z2c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geo Final Topics 6 and 7
#### Problem Statement:
**Find the measure of the numbered angles in the rhombus. The diagram is not to scale.**
In the given diagram, the rhombus is divided into four smaller triangles. The diagram includes the following angles and sides:
- Angle at the top (marked as 44°)
- Four internal angles to be determined (labeled as 1, 2, and 3)
#### Potential Answers:
- **Option A:** \(m∠1 = 90°, \, m∠2 = 44°, \, \text{and} \, m∠3 = 46°\)
- **Option B:** \(m∠1 = 90°, \, m∠2 = 46°, \, \text{and} \, m∠3 = 44°\)
- **Option C:** \(m∠1 = 90°, \, m∠2 = 44°, \, \text{and} \, m∠3 = 44°\)
- **Option D:** \(m∠1 = 90°, \, m∠2 = 44°, \, \text{and} \, m∠3 = 68°\)
### Explanation:
To find the correct measures of the angles labeled 1, 2, and 3 in the rhombus, consider the properties of rhombuses, such as opposite angles being equal and the diagonals bisecting each other at right angles.
#### Additional Notes:
- **Diagram Specifics:** The diagram shows a rhombus with a specific angle of 44° at the top vertex, and the diagonals intersect forming four smaller triangles within the rhombus.
- **Required Knowledge:** Understanding of the properties of rhombuses and how diagonals intersect can help solve this problem correctly.
This problem is a typical example in geometry that tests understanding of angle relationships in quadrilaterals, particularly rhombuses.
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