Proposition I-7

Proposition I-14. If with any straight line, and at a point on it, two straight lines not lying on the same side make the adjacent angles equal to two right angles, the two straight lines will be in a straight line with one another.
Proof.

But the angles CBA and DBA sum to two right angles.

Since the whole is greater than the part (CN-5), it is impossible that EB is in a straight line with CB. Therefore CB is in a straight line with DB, which was to be proved.

QED

Construct two lines at B, CB and DB, for which the angles CBA and DBA sum to two right angles.

Suppose that CB is not in a straight line with DB.

Construct a line BE which is in a straight line with CB.

Then, since CE is a straight line and AB is set upon it, it follows that EBA and CBA equal two right angles.
(prop I-12)

QED

Let AB be the given line.