Why are the four evangelists represented as an angel, a lion, an ox and an eagle?

It is very common in catholic art to find the evangelists represented

The four authors of the Gospels (St. Matthew, St. Mark, St. Luke and St. John) have been symbolically related to the four living creatures of Revelation 4:7:
"The first Living One, like a lion;
the second Viviente, like a steer;
the third Living One has a face like a man;
the living fourth is like an eagle in flight." Rev 4:7.

Traditionally, the four evangelists are represented by four symbols.
The order in which they appear in the New Testament are:
- The angel (a man with wings): Matthew.
- The lion: Marcos.
- The ox: Lucas.
- The eagle: John.

Matthew symbolized himself with an angel (a man with wings) because his gospel begins with the list of the ancestors of Jesus, the Messiah: Mt 1:1-16. This list is of great value for this gospel because it presents Jesus as the son of David (the most important of the kings) and the son of Abraham (the father of God's people).

uan is represented by an eagle, his gaze directed towards the sun, because his Gospel opens with the contemplation of Jesus-God: Jn 1:1.
The Gospel of John was the last to appear, and it was not written in a few days. It was written by John's disciples. One of the characteristics of the Jesus of John's Gospel is this: the Master knows each one of us better than we know ourselves: Jn 1:48. A little further on it says that Jesus "did not need to be told about anyone, for he knew the inner man very well." (Jn 2:25).
The eagle is considered the "solar bird", image of fire, altitude, depth and light; it is the bird that possesses a penetrating sight, comparable to the "all-seeing eye", capable of soaring above the clouds and staring at the sun, so it symbolizes every transcendent state, the highest power, contemplation, genius and heroism.

It is the symbol of spiritual ascension, which keeps her elevated on the heights. The Gospel of John, which Clement of Alexandria called "spiritual gospel", is the most profound, symbolic, contemplative and theological of the four and, in that sense, the one that rises above the others. John's is the only non-synoptic gospel.

Luke has been symbolized by an ox or a bull because his gospel begins with the vision of Zechariah in the Temple, where animals such as oxen, calves and sheep were sacrificed.
Luke's Gospel begins and ends in the Temple; the Acts of the Apostles constitutes the second part of Luke's Gospel.
If in the Gospel we find the way of Jesus, in Acts we have the way of the communities that followed Jesus. The book of Acts ends with Paul's arrival in Rome, a city that, for Luke, represents "the ends of the earth".

Mark is symbolized by a lion because his gospel begins with the preaching of the Baptist in the desert, where there were wild animals.
His gospel was the first to be written (in the decade of the 60's after Christ) and served as a catechetical text for those preparing to receive baptism.
It is the shortest gospel and the fact that it begins by presenting John the Baptist in the desert is very important.
For the people of the Bible, the desert represented, among other things, the place where new projects are forged. This is what the people of God did when they left the slavery of Egypt.