Remember all those pesky geometry classes in high school? Then you'll remember measuring the angle or space between two intersecting lines in "degrees." If you recall that a "right angle" has ninety degrees, give yourself a bonus.
Angle can also mean a biased way of looking at or presenting something. Talk radio stations, for example, often discuss current events with a "political angle." On a far more peaceful note, to angle also means simply to fish, both in the literal sense of trying to catch a fish on a hook or in the metaphorical sense of trying to subtly obtain something without being seen to do so directly, as in, "I'm going to angle for a promotion at work."
Primary Meanings of angle
1. 
nv 
the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians
move or proceed at an angle

2. 
nv 
a biased way of looking at or presenting something
present with a bias

3. 
v 
fish with a hook

Full Definitions of angle
1
n the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians
 Types:
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crotch, fork
the angle formed by the inner sides of the legs where they join the human trunk

axil
the upper angle between an axis and an offshoot such as a branch or leafstalk

helix angle
the constant angle at which a helix cuts the elements of a cylinder or cone

complementary angles
two angles whose sum is a right angle

angular distance
the angular separation between two objects as perceived by an observer

plane angle
an angle formed by two straight lines (in the same plane)

spherical angle
an angle formed at the intersection of the arcs of two great circles

solid angle
an angle formed by three or more planes intersecting at a common point (the vertex)

angle of inclination, inclination
(geometry) the angle formed by the xaxis and a given line (measured counterclockwise from the positive half of the xaxis)

inclination, inclination of an orbit
(astronomy) the angle between the plane of the orbit and the plane of the ecliptic stated in degrees

salient angle
an angle pointing outward; an interior angle of a polygon that is less than 180 degrees

interior angle, internal angle
the angle inside two adjacent sides of a polygon

exterior angle, external angle
the supplement of an interior angle of a polygon

angle of incidence, incidence angle
the angle that a line makes with a line perpendicular to the surface at the point of incidence

angle of reflection
the angle between a reflected ray and a line perpendicular to the reflecting surface at the point of incidence

angle of refraction
the angle between a refracted ray and a line perpendicular to the surface between the two media at the point of refraction

angle of extinction, extinction angle
the angle from its axis that a crystal must be rotated before appearing maximally dark when viewed in polarized light

dogleg
angle that resembles the hind leg of a dog

right angle
the 90 degree angle between two perpendicular lines

oblique angle
an angle that is not a right angle or a multiple of a right angle

reflex angle
an angle greater than 180 degrees (but less than 360)

perigon, round angle
an angle of 360 degrees

cutting angle
the angle between the face of a cutting tool and the surface of the work

angle of dip, dip, inclination, magnetic dip, magnetic inclination
(physics) the angle that a magnetic needle makes with the plane of the horizon

lead
the angle between the direction a gun is aimed and the position of a moving target (correcting for the flight time of the missile)

magnetic declination, magnetic variation, variation
the angle (at a particular location) between magnetic north and true north

AZ, azimuth
the azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridian

polyhedral angle
the space enclosed by three or more planes that intersect in a vertex

face angle
the angle formed by two edges of a polyhedral angle

tilt angle
the angle a rocket makes with the vertical as it curves along its trajectory

vertical angle
either of two equal and opposite angles formed by the intersection of two straight lines

angle of view, view angle
the angle included by a photographic lens

wave angle
the angle of arrival (or departure) of a radio wave with respect to the axis of an antenna array

latitude
the angular distance between an imaginary line around a heavenly body parallel to its equator and the equator itself

longitude
the angular distance between a point on any meridian and the prime meridian at Greenwich

celestial latitude, dec, declination
(astronomy) the angular distance of a celestial body north or to the south of the celestial equator; expressed in degrees; used with right ascension to specify positions on the celestial sphere

RA, celestial longitude, right ascension
(astronomy) the equatorial coordinate specifying the angle, measured eastward along the celestial equator, from the vernal equinox to the intersection of the hour circle that passes through an object in the sky; usually expressed in hours and minutes and seconds; used with declination to specify positions on the celestial sphere

HA, hour angle
(astronomy) the angular distance of a celestial point measured westward along the celestial equator from the zenith crossing; the right ascension for an observer at a particular location and time of day

true anomaly
the angular distance of a point in an orbit past the point of periapsis measured in degrees

reentering angle, reentrant angle
an interior angle of a polygon that is greater than 180 degrees

hip
(architecture) the exterior angle formed by the junction of a sloping side and a sloping end of a roof

angle of attack
the acute angle between the direction of the undisturbed relative wind and the chord of an airfoil

critical angle
the smallest angle of incidence for which light is totally reflected

acute angle
an angle less than 90 degrees but more than 0 degrees

obtuse angle
an angle between 90 and 180 degrees
 Type of:

space
an empty area (usually bounded in some way between things)
v move or proceed at an angle
v to incline or bend from a vertical position
 Types:
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incline, pitch, slope
be at an angle

weather
cause to slope

heel, list
tilt to one side

lean back, recline
move the upper body backwards and down

ascend
slope upwards

stoop
sag, bend, bend over or down

fall
slope downward

climb
slope upward

dip
slope downwards

fall back
fall backwards and down
2
n a biased way of looking at or presenting something
 Synonyms:
 slant
 Type of:

point of view, stand, standpoint, viewpoint
a mental position from which things are viewed
v present with a bias
 Type of:

bias, predetermine
cause to be biased