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Acute angleFrom Latin: acutus - "sharp, pointed"
Definition: Ananglewhose measure is less than 90
Try this Adjust theanglebelow by dragging an orange dot and see how the angle ABC behaves. Note
that it is acute for all angles from zero to (but not including) 90
Obtuse angleFrom Latin: obtusus - "blunt"
Definition: Ananglewhose measure is greater than 90 and less than 180Try this Adjust theanglebelow by dragging the orange dot at A and see how the angle ABC behaves.
Note that it is obtuse for all angles greater than 90 and less than 180
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right angle is ananglethat bisects the angle formed by two halves
of a straight line. More precisely, if arayis placed so that its
endpoint is on a line and the adjacent angles are equal, then they
are right angles.[1]
As a rotation, a right angle corresponds to a
quarter turn (that is, a quarter of a full circle).[2]
Closely related and important geometrical concepts
areperpendicularlines, meaning lines that form right angles at their
point of intersection, andorthogonality, which is the property of
forming right angles, usually applied tovectors. The presence of a
right angle in atriangleis the defining factor forright
triangles,[3]
making the right angles basic to trigonometry.
adjacent angles, often shortened as adj. s, areanglesthathave a common ray coming out of the vertex going between two
other rays, with no overlap of the regions "enclosed" by the two
angles. In other words, they are angles that are side by side, oradjacent.
Vertical Angle a pair ofanglesis said tobe vertical (also opposite andvertically opposite, which is
abbreviated as vert. opp. s[1]) if the angles are formed from twointersectinglinesand the angles are not adjacent. The two angles
share a vertex. Such angles are equal inmeasureand can be
described as "equal" (in the UK or the USA) or "congruent" (in the
USA).
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Complementary angles areangleswhose measures sum to
90. If the two complementary angles are adjacent (i.e. have a
commonvertexand share just one side) their non-shared
sides form aright angle.
InEuclidean geometry, the two acute angles in aright
triangleare complementary, because the sum of internal
angles of a triangle is 180 degrees, and the right angle itself
accounts for ninety degrees.
The adjective complementaryis fromLatincomplementum,
associated with the verb complere, "to fill up". An acute angle
is "filled up" by its complement to form a right angle.
Supplementary angles are pairs ofanglesthat add up to
180degrees. Thus the supplement of an angle ofxdegrees
is an angle of (180
x) degrees.
If the two supplementary angles areadjacent(i.e. have a
commonvertexand share just one side), their non-shared
sides form astraight line. However, supplementary angles do
not have to be on the same line, and can be separated in
space. For example, adjacent angles of aparallelogramare
supplementary, and opposite angles of acyclic
quadrilateral(one whose vertices all fall on a single circle)
are supplementary.
If a point P is exterior to a circle with center O, and if thetangent linesfrom P touch the circle at points T
and Q, then TPQ and TOQ are
supplementary.
Linear Pair of anglesFrom Latin: linearis - "belonging to a line"
Definition: Two angles thatareadjacent(share a leg)
andsupplementary(add up to 180)
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