Mathematic Rule about adjacent angles

Question

Is there a mathematic rule, postulate, theorem, or definition that states the following:

 

Two adjacent equal angles whose sum is 180° are right angles.

 

 

Answer 1

This statement is a simply consequence from the definition of adjacent angles. They have common side. 

 

If angles x and y are adjacent and x=y then, because x+y = 2x= 180⁰, then x = 180/2 = 90⁰.