Postulate: The Protractor Postulate

Given line AB and a point O on line AB. Consider rays OA and OB, as well as all the other rays that can be drawn, with O as an endpoint, on one side of line AB. These rays can be paired with the real numbers between 0 and 180 in such a way that:

Â Â 1. Ray OA is paired with 0, and ray OB is paired with 180.

Â Â 2. If ray OR is paired with a and ray OQ is paired with b,

Â Â Â Â Â then mÃ ROQ = | a - b |.