If a straight line set up on a straight line makes angles, it will make either two right angles or angles equal to two right angles.

For let any straight line $AB$ set up on the straight line $CD$ make the angles $CBA$, $ABD$;I say that the angles $CBA$, $ABD$ are either two right angles or equal to two right angles.Now, if the angle $CBA$ is equal to the angle $ABD$,they are two right angles. [Def. 10]But, if not, let $BE$ be drawn from the point $B$ at right angles to $CD$; [Prop. 1.11]threfore the angles $CBE$, $EBD$ are two right angles.Then, since the angle $CBE$ is equal to the two angles $CBA$, $ABE$,let the angle $EBD$ be added to each;therefore the angles $CBE$, $EBD$ are equal to the three angles $CBA$, $ABE$, $EBD$. [C.N. 2]Again, since the angle $DBA$ is equal to the two angles $DBE$, $EBA$,let the angle $ABC$ be added to each;therefore the angles $DBA$, $ABC$ are equal to the three angles $DBE$, $EBA$, $ABC$. [C.N. 2]But the angles $CBE$, $EBD$ were also proved equal to the same three angles;and things which are equal to the same thing are also equal to one another; [C.N. 1]therefore the angles $CBE$, $EBD$ are also equal to the angles $DBA$, $ABC$.But the angles $CBE$, $EBD$ are two right angles;therefore the angles $DBA$, $ABC$ are also equal to two right angles.Therefore etc.Q.E.D.