angle

noun

1. A figure formed by two rays which start from a common point (a plane angle) or by three planes that intersect (a solid angle).

   “the angle between lines A and B”

2. The measure of such a figure. In the case of a plane angle, this is the ratio (or proportional to the ratio) of the arc length to the radius of a section of a circle cut by the two rays, centered at their common point. In the case of a solid angle, this is the ratio of the surface area to the square of the radius of the section of a sphere.

   “The angle between lines A and B is π/4 radians, or 45 degrees.”

   “The single-imaging optic of the mammalian eye offers some distinct visual advantages. Such lenses can take in photons from a wide range of angles, increasing light sensitivity. They also have high spatial resolution, resolving incoming images in minute detail.”

3. A corner where two walls intersect.

   “an angle of a building”

4. A change in direction.

   “The horse took off at an angle.”

5. A viewpoint; a way of looking at something.

   “In his first book since the 2008 essay collection Natural Acts: A Sidelong View of Science and Nature, David Quammen looks at the natural world from yet another angle: the search for the next human pandemic, what epidemiologists call “the next big one.””

   “For example, if I was trying to repitch an idea to a producer who had already turned it down, I would say something like, "I remember you said you didn't like my idea because there was no women's angle. Well, here's a great one that both of us must have missed during our first conversation."”

6. The focus of a news story.
7. Any of various hesperiid butterflies.
8. (slang)A storyline between two wrestlers, providing the background for and approach to a feud.
9. (slang)An ulterior motive; a scheme or means of benefiting from a situation, usually hidden, often immoral.

   “His angle is that he gets a percentage, but mostly in trade.”

10. A projecting or sharp corner; an angular fragment.

    “though but an angle reached him of the stone”

11. Any of the four cardinal points of an astrological chart: the Ascendant, the Midheaven, the Descendant and the Imum Coeli.
12. A fishhook; tackle for catching fish, consisting of a line, hook, and bait, with or without a rod.

    “Give me mine angle: we'll to the river there.”

    “A fisher next his trembling angle bears.”

13. (historical)A member of a Germanic tribe first mentioned by Tacitus, one of several which invaded Britain and merged to become the Anglo-Saxons; an Anglian.

verb

1. (transitive)To place (something) at an angle.

   “The roof is angled at 15 degrees.”

2. (informal, intransitive)To change direction rapidly.

   “The five ball angled off the nine ball but failed to reach the pocket.”

3. (informal, transitive)To present or argue something in a particular way or from a particular viewpoint.

   “How do you want to angle this when we talk to the client?”

4. (transitive)To hamper (oneself or one's opponent) by leaving the cue ball in the jaws of a pocket such that the surround of the pocket (the "angle") blocks the path from cue ball to object ball.
5. (intransitive)To try to catch fish with a hook and line.
6. (figuratively, informal)To attempt to subtly persuade someone to offer a desired thing.

   “He must be angling for a pay rise.”