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Ch. 3 - An Introduction to Organic Compounds: Nomenclature, Physical Properties, and Structure
Bruice - Organic Chemistry 8th Edition
Bruice8th EditionOrganic ChemistryISBN: 9780135213711당신이 사용하는 게 아니라요?교과서 변경
3장, 문제 43

The bond angles in a regular polygon with n sides are equal to 180° - 360°/n
a. What are the bond angles in a regular octagon?
b. What are the bond angles in a regular nonagon?

검증된 단계별 안내
1
Step 1: Understand the formula for bond angles in a regular polygon. The bond angle is given by the formula: 180° - 360°n, where n is the number of sides of the polygon.
Step 2: For part (a), substitute n = 8 (since an octagon has 8 sides) into the formula. The bond angle becomes: 180° - 360°8.
Step 3: Simplify the fraction 360°8 to find the value of the term to subtract from 180°.
Step 4: For part (b), substitute n = 9 (since a nonagon has 9 sides) into the formula. The bond angle becomes: 180° - 360°9.
Step 5: Simplify the fraction 360°9 to find the value of the term to subtract from 180°.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Polygon Interior Angles

In geometry, the interior angles of a polygon are the angles formed between two adjacent sides. For a regular polygon, all interior angles are equal. The formula for calculating the measure of each interior angle is derived from the total sum of the interior angles, which is (n-2) × 180°, where n is the number of sides.
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Regular Polygon

A regular polygon is a polygon with all sides and all angles equal. This symmetry allows for straightforward calculations of angles and side lengths. For example, in a regular octagon, all eight sides are of equal length, and all interior angles are congruent, making it easier to apply geometric formulas.
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Inscribed Polygon Method

Angle Calculation Formula

The formula for calculating the bond angles in a regular polygon is given by 180° - 360°/n, where n is the number of sides. This formula accounts for the fact that as the number of sides increases, the interior angles approach 180°, resulting in a more 'circle-like' shape. This is crucial for determining the angles in polygons like octagons and nonagons.
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