Szög

Szög (Hungarian for "angle") is a geometric concept defined as the figure formed by two rays that share a common endpoint, called the vertex. The opening between the rays is the size of the angle. An angle can be denoted with the symbol ∠, for example ∠ABC denotes the angle with vertex B formed by BA and BC.

Angles are classified by their size: acute (< 90°), right (= 90°), obtuse (> 90° and < 180°), straight (= 180°), and reflex (> 180° and < 360°). A convex angle is any angle less than 180°, while a reflex angle is greater than 180°. Angles can also be described by orientation, with the concept of oriented angles used in more advanced contexts.

Angles are measured in degrees or radians. A full circle measures 360 degrees or 2π radians. Conversions are straightforward: radians = degrees × π/180, and degrees = radians × 180/π. In many geometric problems, the unit choice depends on convenience and the formulas involved.

Key relationships include that adjacent angles on a straight line sum to 180 degrees, while complementary angles sum to 90 degrees and supplementary angles sum to 180 degrees. When two lines cross, opposite angles (vertical angles) are equal. If two lines are parallel, corresponding angles and alternate interior angles are equal.

In triangles, the interior angles always sum to 180 degrees. In trigonometry, for right triangles, the sine, cosine, and tangent relate an angle to the ratios of the triangle’s side lengths. The concept of szög is foundational in geometry, trigonometry, and many applied sciences.