I was wondering if the angels are made of light, could we see them if we traveled at the speed of light?
All religions including Islam agree that angels in essence are not corporeal beings otherwise not only the Prophets but anyone nearby could normally see them when they appeared to the Prophets to communicate Divine messages or when they descend upon believers to support them without appearing to them in a visible physical form (as they did to believers in the Battle of Badr, as well as to the disciples of Jesus). Nonetheless religious scriptures do not rule out that angels can appear in a visible corporeal form either to Prophets or commons (as in the case of those who appeared to Abraham and people of Lut), but this is evident by both scriptures and our own understanding that angels are normally incorporeal and invisible to us except, as scriptures show, when they are ordered to appear in a physical form to Prophets or ordinary people to fulfill special Divine decrees.
Obviously or not, the reason for Angels' ability to be both visible and invisible, and their ability to assume and take off physical forms is that in their capacity as executors of Divine orders in the natural world, they occupy an intermediary plane between the Divine realm and the natural realm hence assuming some of the characteristics of both.
So considering the incorporeal nature of angels, "light" that is said to constitute their existence can not be a physical being. But even assuming that light that make's up angels is physical light, there is no reason for the connection perceived between the ability to travel at the speed of a being's "building blocks" and the ability to see that being!