### Geo Final Topics 6 and 7#### Problem Statement:**Find the measure of the numbered angles in the rhombus. The diagram is not to scale.**![Diagram of a rhombus](Diagram-of-a-rhombus)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.

Answered: Image /qna-images/answer/c0c3d934-c9ac-4661-a878-3453938e5151.jpg

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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Concept explainers

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.

Question

### Geo Final Topics 6 and 7

#### Problem Statement:
**Find the measure of the numbered angles in the rhombus. The diagram is not to scale.**

![Diagram of a rhombus](Diagram-of-a-rhombus)

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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