WHENEVER we speak about God, we are never using terms in EXACTLY the same way that we use them with regard to creatures (we are using them in a SIMILAR way, but not in precisely the same way....that is, we are using terms, as St. Thomas Aquinas would say, in an "analogous" way, not in an "univocal" way). For, as St. Thomas Aquinas teaches, whenever we speak about God, we are using terms that come from our human experience in creation; but, God is so far beyond His creation that, likewise, He will be so far beyond those terms that we use which derive from His creation.
Thus, when we speak about "anger" with regard to God and "anger" with regard to man (or brute animals), we are not using the term "anger" in exactly the same way (again, we are using "anger" in an "analogous", not "univocal", way). The reason why we use the same term to describe men and God is that there are similarities in the way that angry men act, and the way that God acts in creation when He is said to be "angry". For, when a man is angry, he will tend to act in a way to correct what he perceives to be an injustice (perhaps resorting to violence, if necessary). Likewise, when God is said to be angry, He will tend to act in a way to correct an injustice that He knows is occurring, perhaps resorting to violence (eg., Sodom and Gomorrah; the Plagues in Egypt; the death of Ananias and Sapphira (Acts 5) for lying to Peter; etc.). But, there are differences between an "angry" man and God when He is "angry". For one thing, "anger" in a man is an emotion (stemming from the fact that man has a physical, bodily nature with emotions); but, God, in His divine nature, does not have a body, nor does He have emotions in the true sense (thus, He does not "feel" "anger" like we do). Likewise, for man to feel "angry" implies that there is some weakness in man (there is a real threat or injustice done to him which he seeks to avenge); but, with God, there are no weaknesses, no imperfections, and thus, no possibility of REALLY doing harm to God (for, God is all-powerful and all-perfect for all eternity). Thus, God could never really experience an "unjust" harm done to His Being; could never experience a lessening of His Being or His Perfect, Eternal Happiness. And, thus, God could never be "angry" like we could when we DO experience a real harm done to our person.
Thus, in short, God's "anger" is similar to man's "anger", but not exactly the same.
Having said that, God did become Man in the Person of Jesus Christ, who was clearly angry in certain circumstances (eg., Temple Cleansing in Jerusalem of John 2, et al.; the "Woes" to the Scribes and Pharisees of Matt. 23; etc.). And, so, in Christ, God has experienced the sort of anger that we experienced (with one very important difference: Jesus' anger was NEVER sinful, but always directed to true justice, to true ZEAL. While, our anger, often fueled more by pride than by righteous zeal, is often tainted with sin). May we look to Christ, Our Lord, who, while being "meek and humble of heart" (Matt. 11:28) was also, at the same time, filled with "zeal for His Father's House", and has given us some examples of righteous anger--- that is, anger that is concerned only for the Glory of God and His Church!