Euclid I-23. (pg 18)
Explanation:
Let there exist line AB and angle CDE.
Let C and E be chosen be taken at random and CE joined.
Pick pt F on AB such that AF =DE.
let AG= CD and FG= CE. (Using circle radii and the proposition before this one in the book)
By SSS, these triangles are congruent.
Thus, Angle FAG = angle DCE.
Therefore, a rectilineal angle on a line had been constructed such that it is = to another rectilineal angle.