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?

Verified step by step guidance

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

Key Concepts

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.

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.

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.