I was always taught that Angels could do nothing on their own. They were created to do God's will and had no free will of their own. Then I hear Satan rebelled against God and 1/3 of the Angels followed him. How can this be if they have no free will?

The heavenly angels gladly and completely do the bidding of God. Psalm 103:20-21 [20] Bless the LORD, ye his angels, that excel in strength, that do his commandments, hearkening unto the voice of his word. [21] Bless ye the LORD, all ye his hosts; ye ministers of his, that do his pleasure.
See All... states, "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." Their purpose is to do His commandments, hearken to His voice, and do His pleasure.

However, no scripture declares that angels have no free will. From the fact of the fall of so many of them, they obviously have some form of self- etermination. That is, they have the freedom to remain in that holy estate into which they were placed by creation or to leave their first estate for a lower one. "And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day" (Jude 1:6And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.
See All...). Clearly, they are not robots unable to do anything but obey God.

However, their condition is not like that of man. Man can be redeemed from his fallen state by the applied blood of Jesus Christ. The fallen angels have no means by which they can return to their first estate after they leave it. They will all be cast into the "everlasting fire, prepared for the devil and his angels" (Matthew 25:41Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
See All...). Also, there is no mix of obedience with disobedience in the angels as there often is in regenerate man. The angels in heaven perform the commandments of God with full obedience (Psalm 103:20-21 [20] Bless the LORD, ye his angels, that excel in strength, that do his commandments, hearkening unto the voice of his word. [21] Bless ye the LORD, all ye his hosts; ye ministers of his, that do his pleasure.
See All...). The fallen angels are simply "the angels that sinned" (2Peter 2:4For if God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment;
See All...). No good is seen in them.

We will probably never be able to grasp with fullness the reason for the angels to rebel against God and leave their heavenly estate. They saw God in His absolute glory and holiness. They saw the greatness of His power. What could they hope to gain by a rebellion against such a God? However, scripture does reveal the initial motivation of their rebellion. From a study of Satan and his part in leading the rebellion, we know that their rebellion was fueled by willful pride. Isaiah 14:12-15 [12] How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! [13] For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: [14] I will ascend above the heights of the clouds; I will be like the most High. [15] Yet thou shalt be brought down to hell, to the sides of the pit.
See All... gives important insight into this matter. In this passage, Satan (as Lucifer) states five times, "I will." Especially revealing is his fifth declaration: "I will be like the most High" (Isaiah 14:14I will ascend above the heights of the clouds; I will be like the most High.
See All...). He did not desire to submit to the will and glory of God, but rather wanted to be like God himself.

This was pride. The bishop, or pastor, is not to be "a novice, lest being lifted up with pride he fall into the condemnation of the devil" (1Timothy 3:6Not a novice, lest being lifted up with pride he fall into the condemnation of the devil.
See All...). The devil fell into condemnation because he was lifted up with pride. He refused to submit to the will of the Father, lost his first estate, and has taken many of the angels with him. His "tail drew the third part of the stars of heaven, and did cast them to the earth" (Revelation 12:4And his tail drew the third part of the stars of heaven, and did cast them to the earth: and the dragon stood before the woman which was ready to be delivered, for to devour her child as soon as it was born.
See All...).

The angels do not have a sin nature. We have one because of our descent from Adam. All angels have been directly created by God and must have been created with a holy nature. Therefore, they never have the mix of good and bad often found in men. However, they were created with the ability and responsibility of self-determination. They can choose to leave the estate of heaven by an act of will. Or, they can choose to stay with God. Those who leave, do so in order to be gods. Satan is the "the god of this world" (2Corinthians 4:4In whom the god of this world hath blinded the minds of them which believe not, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them.
See All...). Satan's motivation is further revealed in his temptation of Adam and Eve in the Garden. He told them, "and ye shall be as gods, knowing good and evil" (Genesis 3:5For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.
See All...). That is what moved him to rebel and that is what he used on Eve.

Understanding this helps with another verse. 1Corinthians 11:10For this cause ought the woman to have power on her head because of the angels.
See All... states, "For this cause ought the woman to have power on her head because of the angels." The passage in 1Corinthians is dealing with the outward submission of the woman. Her external act of submission is important "because of the angels." I take that to mean that ladies who submit to their husbands, not because he is any better than her but simply because it is God's way, provide an excellent example to the angels in heaven. If she can submit to her husband with all his faults and problems, then certainly the angels should be able to submit to the Holy God.