Given an angle ABC (with the center in B), you should put the compass with the center in B and make an arc with a length that is more than the double of the angle. There you have the intersections between the arc and the segments BA and BC - let's call the intersections D and E. You should open the compass from D to E and make an arc starting in D which intersects the previous arc - let's call that intersection F. Now you should draw a segment (using the straightedge) which starts in B and passes through F and ends in a new point -let's call that one G- with a length similar to AB and BC. So now you have the angle ABG (with center in B) which is adjacent and congruent to ABC.