There are a multitude of reasons why Jesus is said to be the Messiah. I am not going to list every single one of them in this text. Here are a few that I would like to acknowledge.

Isaiah 53:3-5

Written approximately 700 years before the birth of Jesus about the coming Messiah

3. He was despised and rejected by men, a man of sorrows, and familiar with suffering. Like one from whom men hide their faces he was despised, and we esteemed him not.

4. Surely he took up our infirmities and carried our sorrows, yet we considered him stricken by God, smitten by him, and afflicted.

5. But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was upon him, and by his wounds we are healed.
 

Comment:  Fast forward to Matthew. It sounds like we are talking about the same person.

Matthew 27:21-23

Written in approximately 60 years after the death of Jesus

21."Which of the two do you want me to release to you?" asked the governor.
      "Barabbas," they answered.

22."What shall I do, then, with Jesus who is called Christ?" Pilate asked.
      They all answered, "Crucify him!"

23."Why? What crime has he committed?" asked Pilate.
      But they shouted all the louder, "Crucify him!"

Isaiah 7:13-14

13.Then Isaiah said, "Hear now, you house of David! Is it not enough to try the patience of men? Will you try the patience of my God also?

14.Therefore the Lord himself will give you a sign: The virgin will be with child and will give birth to a son, and will call him Immanuel

Comment: Notice in Matthew that Jesus is a direct descendant of King David which makes him heir to the throne of Isreal. His Mother was also a virgin.

Matthew 1:1-17

The Genealogy of Jesus

1. A record of the genealogy of Jesus Christ the son of David, the son of Abraham:

2. Abraham was the father of Isaac,Isaac the father of Jacob,Jacob the father of Judah and his brothers,

3. Judah the father of Perez and Zerah, whose mother was Tamar,Perez the father of Hezron,Hezron the father of Ram,

4. Ram the father of Amminadab,Amminadab the father of Nahshon,Nahshon the father of Salmon,

5. Salmon the father of Boaz, whose mother was Rahab,Boaz the father of Obed, whose mother was Ruth,Obed the father of Jesse,

6. and Jesse the father of King David.David was the father of Solomon, whose mother had been Uriah's wife,

7. Solomon the father of Rehoboam,Rehoboam the father of Abijah,Abijah the father of Asa,

8. Asa the father of Jehoshaphat,Jehoshaphat the father of Jehoram,Jehoram the father of Uzziah,

9. Uzziah the father of Jotham,Jotham the father of Ahaz,Ahaz the father of Hezekiah,

10. Hezekiah the father of Manasseh,Manasseh the father of Amon,Amon the father of Josiah,
      
11. and Josiah the father of Jeconiah[a] and his brothers at the time of the exile to Babylon.

12. After the exile to Babylon:Jeconiah was the father of Shealtiel,Shealtiel the father of Zerubbabel,
      
13. Zerubbabel the father of Abiud,Abiud the father of Eliakim,Eliakim the father of Azor,

14. Azor the father of Zadok,Zadok the father of Akim,Akim the father of Eliud,

15. Eliud the father of Eleazar,Eleazar the father of Matthan,Matthan the father of Jacob,

16. and Jacob the father of Joseph, the husband of Mary, of whom was born Jesus, who is called Christ.

17. Thus there were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Christ.