Angels are mentioned many times in the Holy books of the Old Testament, which do not form part of the Holy Torah.  The following are a few pertinent Biblical entries from these books.

And ye shall make no league with the inhabitants of this land; ye shall throw down their altars: but ye have not obeyed my voice: why have ye done this?

Wherefore I also said, I will not drive them out from before you; but they shall be as thorns in your sides, and their gods shall be a snare unto you.

And it came to pass, when the ANGEL of the LORD spake these words unto all the children of Israel, that the people lifted up their voice, and wept.

And they called the name of that place Bochim: and they sacrificed there unto the LORD."

 
"And there came an ANGEL of the LORD, and sat under an oak which was in Ophrah, that pertained unto Joash the Abiezrite: and his son Gideon threshed wheat by the winepress, to hide it from the Midianites.

And the ANGEL of the LORD appeared unto him, and said unto him, The LORD is with thee, thou mighty man of valour........."

"And Gideon went in, and made ready a kid, and unleavened cakes of an ephah of flour: the flesh he put in a basket, and he put the broth in a pot, and brought it out unto him under the oak, and presented it.

And the ANGEL of God said unto him, Take the flesh and the unleavened cakes, and lay them upon this rock, and pour out the broth. And he did so.  Then the ANGEL of the LORD put forth the end of the staff that was in his hand, and touched the flesh and the unleavened cakes; and there rose up fire out of the rock, and consumed the flesh and the unleavened cakes. Then the ANGEL of the LORD departed out of his sight.

And when Gideon perceived that he was an ANGEL of the LORD, Gideon said, Alas, O LORD God! for I have seen an ANGEL of the LORD face to face.

And the LORD said unto him, Peace be unto thee; fear not: thou shalt not die."

And the ANGEL of the LORD appeared unto the woman, and said unto her, Behold now, thou art barren, and bearest not: but thou shalt conceive, and bear a son....."

"Then the woman came and told her husband, saying, A man of God came unto me, and his countenance was like the countenance of an ANGEL of God, very terrible: but I asked him not whence he was, neither told he me his name:

But he said unto me, Behold, thou shalt conceive, and bear a son....

Then Manoah intreated the LORD, and said, O my Lord, let the man of God which thou didst send come again unto us, and teach us what we shall do unto the child that shall be born.  And God hearkened to the voice of Manoah; and the ANGEL of God came again unto the woman as she sat in the field: but Manoah her husband was not with her. And the woman made haste, and ran, and shewed her husband, and said unto him, Behold, the man hath appeared unto me, that came unto me the other day. And Manoah arose, and went after his wife, and came to the man, and said unto him, Art thou the man that spakest unto the woman? And he said, I am.

And Manoah said, Now let thy words come to pass. How shall we order the child, and how shall we do unto him?......

And the ANGEL of the LORD said unto Manoah, Though thou detain me, I will not eat of thy bread: and if thou wilt offer a burnt offering, thou must offer it unto the LORD. For Manoah knew not that he was an ANGEL of the LORD.

And Manoah said unto the ANGEL of the LORD, What is thy name, that when thy sayings come to pass we may do thee honour?

And the ANGEL of the LORD said unto him, Why askest thou thus after my name, seeing it is secret?

So Manoah took a kid with a meat offering, and offered it upon a rock unto the LORD: and the ANGEL did  wonderously; and Manoah and his wife looked on. For it came to pass, when the flame went up toward heaven from off the altar, that the ANGEL of the LORD ascended in the flame of the altar. And Manoah and his wife looked on it, and fell on their faces to the ground."

And the ANGEL of the LORD stood by the threshing floor of Ornan  the Jebusite. And David lifted up his eyes, and saw the ANGEL of the LORD stand between the earth and the heaven, having a drawn sword in his hand stretched out over Jerusalem. Then David and the elders of Israel, who were clothed in sackcloth, fell upon their faces."

Out of the mouth of babes and sucklings hast thou ordained strength because of thine enemies, that thou mightest still the enemy and the avenger.

When I consider thy heavens, the work of thy fingers, the moon and the stars, which thou hast ordained;

What is man, that thou art mindful of him? and the son of man, that thou visitest him?

For thou hast made him a little lower than the ANGELS, and hast crowned him with glory and honour."

Why leap ye, ye high hills? this is the hill which God desireth to dwell in; yea, the LORD will dwell in it for ever.

The chariots of God are twenty thousand, even thousands of ANGELS: the Lord is among them, as in Sinai, in the holy place."

I will say of the LORD, He is my refuge and my fortress: my God; in him will I trust........

Because thou hast made the LORD, which is my refuge, even the most High, thy habitation;

There shall no evil befall thee, neither shall any plague come nigh thy dwelling.

For he shall give his ANGELS charge over thee, to keep thee in all thy ways.

They shall bear thee up in their hands, lest thou dash thy foot against a stone.

Thou shalt tread upon the lion and adder: the young lion and the dragon shalt thou trample under feet.

Because he hath set his love upon me, therefore will I deliver him: I will set him on high, because he hath known my name.

He shall call upon me, and I will answer him: I will be with him in trouble; I will deliver him, and honour him.

With long life will I satisfy him, and shew him my salvation."

Bless the LORD, ye his ANGELS, that excel in strength, that do his commandments, hearkening unto the voice of his word.

Bless ye the LORD, all ye his hosts; ye ministers of his, that do his pleasure.

Bless the LORD, all his works in all places of his dominion: bless the LORD, O my soul."

Praise ye the LORD from the heavens: praise him in the heights.

Praise ye him, all his ANGELS: praise ye him, all his hosts.

Praise ye him, sun and moon: praise him, all ye stars of light.

Praise him, ye heavens of heavens, and ye waters that be above the heavens.

Let them praise the name of the LORD: for he commanded, and they were created."