Adjacent Angles Geometry by andyikumar

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									                       Adjacent Angles Geometry

Adjacent Angles Geometry
In geometry, adjacent angles, often shortened as adj. ∠s, are angles that have 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, or adjacent. The word “adjacent” means
“next” or “neighboring”. Adjacent angles are angles just next to each other. Adjacent angles share a
common vertex and a common side, but do not overlap. In the mathematics, angles are usually
considered in the Euclidean plane but in some of the case angles are also defined in non- Euclidean
geometry. In the mathematics angles are used to determine the measurement of an angle or of a
rotation. The word angle comes from the Latin word ‘angulus’ which mean refers to ‘a corner’. In the
mathematical term, an angle with the measurement can be represented by the symbol (‘ ∠‘).

Complementary adjacent angles ;-

A pair of angles is complementary if the sum of their measures is 90°.
A pair of angles is supplementary if the sum of their measures is 180°.
An angle with a ray connected to a common point down the center. In geometry, two angles are
adjacent angles if they share a common vertex and side, but have no common interior points.


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Complementary Angles

In geometry, complementary angles are angles whose measures sum to 90°.If the two complementary
angles are adjacent (i.e. have a common vertex and share just one side) their non-shared sides form a
right angle. In Euclidean geometry, the two acute angles in a right triangle are complementary, because
the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety
degrees. The adjective complementary is from Latin complementum, associated with the verb
complere, "to fill up". An acute angle is "filled up" by its complement to form a right angle.

Trigonometric ratios ;- The sine of an angle equals the cosine of its complementary angle. It is
therefore true that, if angles A and B are complementary, , and . The tangent of an angle equals the
cotangent of its complementary angle. The tangents of complementary angles are reciprocals of each
other. The secant of an angle equals the cosecant of its complementary angle. The prefix "co-" in the
names of some trigonometric ratios refers to the word "complementary".

Supplementary Angles

Supplementary angles are pairs of angles that add up to 180 degrees. Thus the supplement of an angle
of x degrees is an angle of (180 − x) degrees. If the two supplementary angles are adjacent (i.e. have a
common vertex and share just one side), their non-shared sides form a straight line. However,
supplementary angles do not have to be on the same line, and can be separated in space. For example,
adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic 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 the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are
supplementary.

Trigonometric ratios ;- The sines of supplementary angles are equal. Their cosines and tangents
(unless undefined) are equal in magnitude but have opposite signs.




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