TeXipedia

angle

Denotes a geometric angle formed by two rays or lines meeting at a vertex.

Overview

Essential in geometry, trigonometry, and mathematical proofs where angle measurements and relationships need to be discussed. Commonly appears in:

  • Euclidean geometry proofs and constructions
  • Triangle calculations and angle theorems
  • Vector analysis when describing orientations
  • Physics problems involving forces and directions

Often used alongside measure notation and degree symbols to specify exact angle values or when referencing specific angles in geometric figures.

Examples

Marking an angle in a geometric triangle.

△ABC has ∠ABC=90∘\triangle ABC \text{ has } \angle ABC = 90^\circ 
\triangle ABC \text{ has } \angle ABC = 90^\circ

Specifying multiple angles in a polygon.

∠A=60∘,∠B=60∘,∠C=60∘\angle A = 60^\circ, \angle B = 60^\circ, \angle C = 60^\circ 
\angle A = 60^\circ, \angle B = 60^\circ, \angle C = 60^\circ

Using angle in a trigonometric equation.

sin⁡(∠θ)=oppositehypotenuse\sin(\angle \theta) = \frac{\text{opposite}}{\text{hypotenuse}} 
\sin(\angle \theta) = \frac{\text{opposite}}{\text{hypotenuse}}