A gemstone in the shape of a rhombus has the measurements shown. Match the measures with the angles. 4mm 4mm 28° 4mm 4mm 13o ... ... ... NEXT 16 PREV 11 12 13 14

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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### Geometry Problem: Identifying Angles in a Geometric Figure

#### Diagram Explanation:
The image presents a geometric figure consisting of a rhombus-like shape segmented by a few lines and angles. Key details of the diagram are as follows:

1. **Annotated Angle:** The top-left angle of the rhombus-like shape is labeled as 28°.
2. **Side Lengths:** Each side of the rhombus-like shape measures 4mm.
3. **Points and Holes:** The figure features three points marked by red circles situated to the right of the shape. A section is also cut out of the shape toward the top right.
4. **Lines:** Diagonal and horizontal lines divide the figure, connecting different points within and on the boundary of the shape.

#### Task:
You are required to identify and select the measure of an angle through multiple-choice answers provided in the bottom section of the image.

#### Options Provided:
- 25°
- 28°
- 56°
- 62°
- 90°
- 124°

#### Navigation:
At the bottom of the image, navigation is enabled by a pink "PREV" button, and numerical page indicators range from 11 to 16, with the current page being 15.

This setup is typical for a practice problem in an online educational platform for geometry, where the user needs to identify or confirm the measure of a specific angle within the geometric figure provided.

### Instructions:
- Carefully observe the geometric figure and understand its properties.
- Use the given information about side lengths and the labeled angle to deduce further angles in the figure.
- Select the correct angle measure from the provided multiple-choice options.

This exercise helps in understanding geometry concepts, particularly the properties of angles within specific shapes.
Transcribed Image Text:### Geometry Problem: Identifying Angles in a Geometric Figure #### Diagram Explanation: The image presents a geometric figure consisting of a rhombus-like shape segmented by a few lines and angles. Key details of the diagram are as follows: 1. **Annotated Angle:** The top-left angle of the rhombus-like shape is labeled as 28°. 2. **Side Lengths:** Each side of the rhombus-like shape measures 4mm. 3. **Points and Holes:** The figure features three points marked by red circles situated to the right of the shape. A section is also cut out of the shape toward the top right. 4. **Lines:** Diagonal and horizontal lines divide the figure, connecting different points within and on the boundary of the shape. #### Task: You are required to identify and select the measure of an angle through multiple-choice answers provided in the bottom section of the image. #### Options Provided: - 25° - 28° - 56° - 62° - 90° - 124° #### Navigation: At the bottom of the image, navigation is enabled by a pink "PREV" button, and numerical page indicators range from 11 to 16, with the current page being 15. This setup is typical for a practice problem in an online educational platform for geometry, where the user needs to identify or confirm the measure of a specific angle within the geometric figure provided. ### Instructions: - Carefully observe the geometric figure and understand its properties. - Use the given information about side lengths and the labeled angle to deduce further angles in the figure. - Select the correct angle measure from the provided multiple-choice options. This exercise helps in understanding geometry concepts, particularly the properties of angles within specific shapes.
### Understanding Rhombus Geometry: A Gemstone Example

#### Problem Statement:
A gemstone in the shape of a rhombus has the measurements shown. Match the measures with the angles.

#### Diagram Explanation:
The diagram depicts a rhombus with sides of 4 mm each. The following measurements are highlighted:

- One of the internal angles is given as 28°.
- The rhombus is divided into smaller sections with dotted lines representing additional lengths and angles to be determined.

#### Steps to Match Measures with Angles:
Since the rhombus has some given measurements and properties of angles, extend the properties of rhombuses to match the angles correctly.

1. **Properties of a Rhombus:**
   - All sides are of equal length.
   - Opposite angles are equal.
   - Adjacent angles summing up to 180°.
   - Diagonals bisect each other at right angles and bisect the angles from which they are drawn.

2. **Given Measurements:**
   - Side length = 4 mm
   - Angle = 28°

3. **Analysis:**
   - By the property of a rhombus, if one angle is 28°, the adjacent angle would be 180° - 28° = 152°.
   - Diagonals bisect the angles; therefore, each angle is divided into two equal parts.

#### Conclusion:
Use these properties and calculations to match the remaining angles.

#### Navigation:
To continue with this exercise, use the "PREV" and "NEXT" buttons to move between questions. This is question 15 of 25 in your session. Keep an eye on the progress bar to track your completion.

For additional assistance or clarifications, please refer to geometry resources or ask your teacher for guidance.
Transcribed Image Text:### Understanding Rhombus Geometry: A Gemstone Example #### Problem Statement: A gemstone in the shape of a rhombus has the measurements shown. Match the measures with the angles. #### Diagram Explanation: The diagram depicts a rhombus with sides of 4 mm each. The following measurements are highlighted: - One of the internal angles is given as 28°. - The rhombus is divided into smaller sections with dotted lines representing additional lengths and angles to be determined. #### Steps to Match Measures with Angles: Since the rhombus has some given measurements and properties of angles, extend the properties of rhombuses to match the angles correctly. 1. **Properties of a Rhombus:** - All sides are of equal length. - Opposite angles are equal. - Adjacent angles summing up to 180°. - Diagonals bisect each other at right angles and bisect the angles from which they are drawn. 2. **Given Measurements:** - Side length = 4 mm - Angle = 28° 3. **Analysis:** - By the property of a rhombus, if one angle is 28°, the adjacent angle would be 180° - 28° = 152°. - Diagonals bisect the angles; therefore, each angle is divided into two equal parts. #### Conclusion: Use these properties and calculations to match the remaining angles. #### Navigation: To continue with this exercise, use the "PREV" and "NEXT" buttons to move between questions. This is question 15 of 25 in your session. Keep an eye on the progress bar to track your completion. For additional assistance or clarifications, please refer to geometry resources or ask your teacher for guidance.
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