There are 72 degrees in one fifth of a whole turn.
Understanding Angles and Turns
A whole turn represents a complete rotation around a point, which is conventionally measured as 360 degrees (°). Angles can be expressed in various units, including turns, degrees, and radians.
To find the number of degrees in a fraction of a whole turn, you simply multiply the fraction by 360 degrees.
- Calculation:
- Whole turn = 360°
- One fifth of a whole turn = (1/5) × 360°
- One fifth of a whole turn = 72°
This means that if you rotate an object through one-fifth of a full circle, it will have moved through an angle of 72 degrees.
Common Angle Equivalents
Here's a quick reference for common fractions of a turn and their corresponding degree measures:
| Turn | Radians | Degrees |
|---|---|---|
| 1/5 turn | 𝜏/5 rad | 72° |
| 1/4 turn | 𝜏/4 rad | 90° |
| 1/3 turn | 𝜏/3 rad | 120° |
| 2/5 turn | 2𝜏/5 rad | 144° |
| 1 whole turn | 𝜏 rad | 360° |
(Note: 𝜏 (tau) is equivalent to 2π, representing one whole turn in radians, approximately 6.283 radians.)
Practical Applications
Understanding these conversions is fundamental in many fields, including:
- Geometry: For calculating angles within polygons or sectors of a circle.
- Navigation: In determining bearings and directions.
- Engineering: For designing rotating machinery or understanding material stress under torsion.
- Computer Graphics: In programming rotations for 3D models and animations.
Angles are a universal way to describe rotation and orientation, making these conversions crucial for accurate measurements and calculations.
