These two words are easy to confuse because they include the same letters and are almost identical in spelling. Both words are nouns, but the angle can also be a verb. When the word angel is used, it is about a celestial being.
A common phrase including the word is "My guardian angel," which often represents a person that has passed on and is watching down from heaven. The word angel is used both in math and in philosophy. In math, angles are relationships between two lines. In philosophy, an angle is a person's viewpoint on an idea or topic.