What is the measure of a central, interior, and exterior angle in a regular octagon? Please help ASAP!
there would be 8 equal central angles, each one is 360/8 °
For a regular n-polygon the sum of the interior angle is 180(n-2)°
each exterior angle is 360/n°
135
To find the measure of a central, interior, and exterior angle in a regular octagon, we need to understand their definitions and relationships.
1. Central angle: A central angle is formed by two radii of a circle intersecting at the center. In a regular polygon, each central angle is the same. To find the measure of a central angle, divide 360 degrees by the number of sides in the polygon.
For a regular octagon (an eight-sided polygon), the measure of each central angle is 360 degrees divided by 8, which is 45 degrees.
2. Interior angle: An interior angle is formed by two sides of a polygon. In a regular polygon, all interior angles are equal. To find the measure of an interior angle in a regular polygon, use the formula: (n-2) × 180 degrees ÷ n, where n is the number of sides.
In the case of a regular octagon, the formula becomes (8-2) × 180 degrees ÷ 8, which simplifies to 135 degrees.
3. Exterior angle: An exterior angle is formed by extending one of the sides of a polygon. In a regular polygon, all exterior angles are equal. The measure of an exterior angle is simply the supplementary angle to the interior angle.
Therefore, in a regular octagon, the exterior angle measures 180 degrees minus 135 degrees, which equals 45 degrees.
To summarize:
- Measure of a central angle in a regular octagon: 45 degrees
- Measure of an interior angle in a regular octagon: 135 degrees
- Measure of an exterior angle in a regular octagon: 45 degrees