Just like the trimmings on the Rosary, some like to add little prayers onto the Angelus. For instance, especially on Saturdays, one may append three Gloria Patri's, in thanksgiving to the Blessed Trinity for Our Lady's glorious privileges; others like to say the prayer to one's Guardian Angel ("Angel of God, my guardian dear, / To whom God's love commits me here, / Ever this day [night] be at my side, / To light and guard, to rule and guide. Amen." – Angele Dei, qui custos es mei, me tibi commissum pietate superna, hodie [hac nocte] illumina, custodi, rege, et guberna. Amen.); I believe in Italy even the De Profundis, with versicles and collect, are added, in order to pray for the dead (I prefer to do this separately; there was a custom to do so at 9pm daily; will post on this!).
Those familiar with the Breviary will recognize that the Collect Gratiam tuam quæsumus is used throughout Advent, together with the versicle Angelus Domini nuntiavit, to accompany the seasonal Marian anthem Alma Redemptoris Mater.
I often recall, when praying the Angelus and ending with its Collect, considering its phrase "may, by His passion and cross, be brought to the glory of His resurrection", the words of St Paul (Philippians iii, 10-11):
Furthermore, in the Traditional Liturgy, the Mass of Our Lady in Advent has the Collect Deus qui de beatæ Mariæ, Secret In mentibus nostris, and Postcommunion Gratiam tuam quæsumus (yes, the very same as the collect of the Angelus). These three are so beautiful, so pregnant with meaning (I say so deliberately), that they make a great meditation in preparation for Christmas; see the last post for details of the last of them, but here are the first two (from my 1954 St Andrew Daily Missal):
Deus, qui de beatæ Mariæ Virginis utero Verbum tuum, Angelo nuntiante, carnem suscipere voluisti: præsta supplicibus tuis: ut, qui vere eam Genitricem Dei credimus, ejus apud te intercessionibus adjuvemur. Per eumdem Christum Dominum nostrum. R/. Amen.
(O God, Who hast willed that Thy Word should take flesh, at the message of an Angel, in the womb of the blessed Virgin Mary, grant to us Thy supplicants, that we who believe her to be truly the Mother of God may be helped by her intercession with Thee. Thro' the same Christ our Lord. R/. Amen.)
In mentibus nostris, quæsumus, Domine, veræ fidei sacramenta confirma: ut, qui conceptum de Virgine Deum verum et hominem confitemur; per ejus salutiferæ resurrectionis potentiam, ad æternam mereamur pervenire lætitiam. Per eumdem Christum Dominum nostrum. R/. Amen.
(We beseech Thee, O Lord, to strengthen in our minds the mysteries of the true faith; that we who confess Him, Who was conceived of the Virgin, to be true God and man, may by the power of His saving resurrection, merit to attain eternal joy. Thro' the same Christ our Lord. R/. Amen.)