Question

angle
an·gle
I
 /ˈæŋgəl/  noun  ,  pl   an·gles [  count  ]
  1 a : the difference between the direction of two lines or surfaces that come together : the space or shape formed when two lines or surfaces meet each other
   The two lines form a sharp angle. = The two lines meet/intersect at a sharp angle (to each other).
   The two lines meet at a 30-degree angle to each other. = There is a 30-degree angle between the two lines.
   The lines are at sharp angles to each other.
  — see also right angle
  1 b
  — used to describe a surface that is not level
   The hill slopes down/up at an angle of about 30 degrees.
  1 c
  — used to describe something that leans or goes to the side rather than straight up or directly forward
   The pole stood at an angle.
   The road goes off at a sharp/slight angle to the right/left.
   The rays of light shone through the window at an angle.
  2 : the position from which something is approached, looked at, etc.
   Critics love the clever camera angles the director used in the film.
   She took pictures of the same scene from several different angles.
   The soldiers were being attacked from every angle.
  3 : a way of thinking about, describing, or discussing something
   We need to approach the problem from a new/different angle.
   They considered the question from all angles.
   The reporter tried to work that angle into his story.
  4 chiefly US, informal
  4 a : a secret and often improper reason for doing something
   I don't trust that guy, but I can't figure out what his angle is yet.
  4 b : a clever and often improper way of doing or getting something
   a salesman who's always looking for an angle [=looking for a way to convince people to buy the things he is selling]
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II
  verb  , angles, an·gled, an·gling /ˈæŋglıŋ/
  1 : to turn, move, or point something so that it is not straight or flat
   [  + obj  ] One spotlight was put high in the corner and angled [=pointed] down toward the floor.
    The seats in the theater were angled so that we were looking almost straight up.
    The road was angled down toward the river.
   [  no obj  ] The road angled [=sloped] down toward the river.
  2 [  + obj  ] : to present (something, such as a news story) in a particular way or from a particular point of view
   You should try to angle the story so that it appeals to younger readers.
  — often used as (be) angled
   The story was angled to appeal to younger readers.
 — compare angle, 3
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III
  verb  , angles, angled, angling [  no obj  ]
  1 : to fish with a hook and line
   go angling for trout
  — see also angler, angling
  2 informal : to try to get what you want in a clever or indirect way
   She's been angling to get a promotion.
  — usually + for
   She's angling for a promotion.
   They're all angling for a place on the committee.
 — compare angle, 2