### Understanding Rotation Angles in Regular Polygons#### Problem 9.3.35:**Prompt:**Point O is the center of the regular nonagon shown at the right.Find the angle of rotation about O that maps D to I.**Solution Space:**A _____° rotation about O maps D to I.**Answer Submission:**Enter your answer in the answer box and then click Check Answer.---#### Diagram Explanation:The diagram consists of a regular nonagon (a nine-sided polygon) with the center labeled as point O. The vertices of the nonagon are labeled in a clockwise manner starting from vertex A. The complete sequence is:- A- B- C- D- E- F- G- H- I#### Calculating the Angle of Rotation:To find the angle of rotation that maps vertex D to vertex I, we need to determine the number of vertices between D and I and the angle subtended per vertex in the nonagon.1. **Total Internal Angles in Nonagon:** - A regular nonagon has 9 sides. - The total internal angles of a polygon = (n - 2) × 180° - For a nonagon: (9 - 2) × 180° = 7 × 180° = 1260°2. **Angle per Vertex in Regular Nonagon:** - Since it’s a regular polygon, the rotation to map a vertex to the next adjacent vertex is equal. - Each internal angle at the center = 360° / number of sides - For nonagon: 360° / 9 = 40°3. **Distance from D to I:** - Count the vertices from D to I in a clockwise direction: - D → E → F → G → H → I - Number of steps = 54. **Total Rotation Angle:** - Total rotation angle = steps × angle per step - Total rotation angle = 5 × 40° = 200°Hence, a 200° rotation about point O maps point D to point I.**Final Answer:**A **200°** rotation about O maps D to I.---**Note for Students:**Understanding how to calculate rotation angles in regular polygons is fundamental in geometry. Ensure you are comfortable with dividing the total degrees around a point (360

To determine the angle of rotation about O.

Answered: 9.3.35 Point O is the center of the…

9.3.35 Point O is the center of the regular nonagon shown at the right. A B. Find the angle of rotation about O that maps D to I. H A rotation about O maps D to I.

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

### Understanding Rotation Angles in Regular Polygons

#### Problem 9.3.35:

**Prompt:**
Point O is the center of the regular nonagon shown at the right.

Find the angle of rotation about O that maps D to I.

**Solution Space:**
A _____° rotation about O maps D to I.

**Answer Submission:**
Enter your answer in the answer box and then click Check Answer.

---

#### Diagram Explanation:
The diagram consists of a regular nonagon (a nine-sided polygon) with the center labeled as point O. The vertices of the nonagon are labeled in a clockwise manner starting from vertex A. The complete sequence is:
- A
- B
- C
- D
- E
- F
- G
- H
- I

#### Calculating the Angle of Rotation:
To find the angle of rotation that maps vertex D to vertex I, we need to determine the number of vertices between D and I and the angle subtended per vertex in the nonagon.

1. **Total Internal Angles in Nonagon:**
- A regular nonagon has 9 sides.
- The total internal angles of a polygon = (n - 2) × 180°
- For a nonagon: (9 - 2) × 180° = 7 × 180° = 1260°

2. **Angle per Vertex in Regular Nonagon:**
- Since it’s a regular polygon, the rotation to map a vertex to the next adjacent vertex is equal.
- Each internal angle at the center = 360° / number of sides
- For nonagon: 360° / 9 = 40°

3. **Distance from D to I:**
- Count the vertices from D to I in a clockwise direction:
- D → E → F → G → H → I
- Number of steps = 5

4. **Total Rotation Angle:**
- Total rotation angle = steps × angle per step
- Total rotation angle = 5 × 40° = 200°

Hence, a 200° rotation about point O maps point D to point I.

**Final Answer:**
A **200°** rotation about O maps D to I.

---

**Note for Students:**
Understanding how to calculate rotation angles in regular polygons is fundamental in geometry. Ensure you are comfortable with dividing the total degrees around a point (360

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