It was clear to the people at the time that Jesus was claiming to be God, not merely an angel or something lesser.
Mark 14:61-64
>61But he held his peace, and answered nothing. Again the high priest asked him, and said unto him, Art thou the Christ, the Son of the Blessed? 62And Jesus said, I am: and ye shall see the Son of man sitting on the right hand of power, and coming in the clouds of heaven. 63Then the high priest rent his clothes, and saith, What need we any further witnesses? 64Ye have heard the blasphemy: what think ye? And they all condemned him to be guilty of death.
What Jesus said there is a reference to Daniel 7:13-14.
>13 I saw in the night visions, and, behold, one like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him.
>14 And there was given him dominion, and glory, and a kingdom, that all people, nations, and languages, should serve him: his dominion is an everlasting dominion, which shall not pass away, and his kingdom that which shall not be destroyed.
A king with an everlasting dominion, served by all peoples, nations, and languages, can only be God. This "blasphemy", of Jesus claiming to be God, is the reason why they put him to death. The high priest would have perfectly understood the reference. Also the expressions "the Blessed One" and "the power (of God)" are Jewish substitutes for using the name of God.