All of the evidences that prove the existence of Allah also prove the existence of angels
It is possible and true to use all of the evidences that prove the existence of Allah in order to prove the existence of angels. Since Allah exists, the existence of angels is compulsory. Is it at all possible that Allah, who is the owner of this universe, should cause creatures to speak with one another in hundreds of thousands languages, that He should listen to their speech, know them, and He Himself should not speak? God forbid! Not to speak is a deficiency. Allah is free and away from deficiencies. Since He spoke, He definitely created angels that would communicate with Him because Allah talked to His human prophets through angels. So, all of the evidences that prove the existence of Allah and His attribute of speech prove and necessitate the existence of angels that He addresses. Only Allah can know the true nature of the word of Allah; it is unknown to us.