A first way is considering opposite angles:
- Pick a point, [tex] O [/tex]
- Draw two rays [tex] r,s [/tex] starting from [tex] O [/tex]
- Let [tex] \alpha [/tex] be the angle between [tex] r [/tex] and [tex] s [/tex]
- Elongate both [tex] r [/tex] and [tex] s [/tex] with respect to [tex] O [/tex] to obtain the rays [tex] r' [/tex] and [tex] s' [/tex]
- The angle between [tex] r' [/tex] and [tex] s' [/tex] is also [tex] \alpha [/tex]
Alternatively, you can start with a given angle, and then draw its bisector. By definition, the bisector cuts a given angle in two equal parts, so you divide an angle [tex] \alpha [/tex] in two parts, both measuring [tex] \frac{\alpha}{2} [/tex]
