Angles are fundamental geometric figures formed by two rays that share a common endpoint. They are essential in mathematics, engineering, navigation, and many other fields. In this guide, we'll explore different types of angles, how they're measured, and their practical applications.
What is an Angle?
An angle is formed when two straight lines or rays meet at a common point called the vertex. The amount of rotation between the two rays is what we measure as the angle.
Key Components:
- Vertex — The common endpoint where two rays meet
- Arms/Rays — The two straight lines that form the angle
- Measure — Rotation between arms, typically in degrees or radians
Measuring Angles
Angles can be measured in several different units:
- Degrees (°) — Full circle is 360°
- Radians (rad) — Full circle is 2π radians
- Gradians (grad) — Full circle is 400 gradians
- Mils (mil) — Military use; 6400 mils ≈ 360° (NATO)
Types of Angles
By Measurement
- Acute — Less than 90°
- Right — Exactly 90°
- Obtuse — Between 90° and 180°
- Straight — Exactly 180°
- Reflex — Between 180° and 360°
- Full rotation — Exactly 360°
By Relationship
- Complementary — Sum to 90°
- Supplementary — Sum to 180°
- Adjacent — Share a vertex and a side
- Vertical — Opposite angles from intersecting lines
Tools for Measuring Angles
Protractor
Semicircular tool with degrees to measure/draw angles.
Bevel Gauge
Transfers angles in woodworking/metalworking.
Theodolite
Precision instrument for surveying in horizontal/vertical planes.
Applications of Angles
Architecture & Construction
- Roof pitch and stair angles
- Structural support calculations
- Window and door installations
Navigation
- Compass bearings
- Flight paths
- Marine navigation
Technology
- Camera field of view
- Robotic arm movements
- 3D modeling and animation
Sports
- Golf club face angle
- Basketball shot trajectory
- Ski and snowboard edges
Did You Know?
Dividing a circle into 360 degrees dates to Babylonian astronomers and their base‑60 system; the sun appears to move ~1° per day.
Converting Between Angle Units
| From | To | Conversion |
|---|---|---|
| Degrees | Radians | rad = deg × (π/180) |
| Radians | Degrees | deg = rad × (180/π) |
| Degrees | Gradians | grad = deg × (10/9) |
| Radians | Gradians | grad = rad × (200/π) |
Practical Tip:
In programming, check whether functions expect degrees or radians. Most trig functions use radians by default.