An angle is a geometrical shape formed by connecting two rays at their endpoints. Angles can be represented by three letters, where the middle letter indicates the vertex. Common symbols used for angles include Greek letters such as θ, α, β, etc. For instance, ∠ABC denotes angle B.
In geometry, there are primarily six types of angles, each with distinct properties:
| Type of Angle | Description |
|---|---|
| Acute Angle | Less than 90° |
| Obtuse Angle | Greater than 90° but less than 180° |
| Right Angle | Exactly 90° |
| Straight Angle | Exactly 180° |
| Reflex Angle | Greater than 180° but less than 360° |
| Full Rotation | Exactly 360° |
In polygons such as triangles, quadrilaterals, pentagons, and hexagons, we distinguish between interior and exterior angles. Interior angles are located within the polygon, while exterior angles are formed outside, between a side and a line extended from an adjacent side.
Positive angles are measured in the anti-clockwise direction, while negative angles are measured clockwise.
Angles can be measured using various units:
Represented by °, degrees originated from the Babylonian base-60 system. A complete rotation is 360°. One degree is further divided into minutes (1' = 1/60°) and seconds (1" = 1/60'). Thus:
1° = 60′ = 3600”
The radian is the SI unit for angles, commonly used in calculus. It is defined by the arc length on a unit circle. One complete circle is equivalent to 2π radians. Therefore:
1 radian = 180°/π
Gradians, also known as gon or grade, measure angles where a complete rotation equals 400 gradians.
Use a protractor to draw angles measuring:
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