Adjacent AnglesAdjacent Angles
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.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.
In a right triangle, the two smaller angles are always complementary. (Why? - one angle is 90 and all
three add up to 180. Therefore the two smaller ones must add to 90 and so are complementary by
definition). See the page on right triangles and convince yourself that this is true.Similar in concept are
supplementary angles, which add up to 180.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.Know More About :-Commutative Property of Addition Math.Edurite.comPage : 1/3
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-", as in co pilot in the names of some
trigonometric ratios refers to the word "complementary".
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 TP
Q and T
OQ are supplementary.The sines of supplementary angles are equal. Their
cosines and tangents (unless undefined) are equal in magnitude but have opposite signs.
In geometry, a pair of angles is said to be vertical (also opposite and vertically opposite, which is
abbreviated as vert. opp. s[
1]) if the angles are formed from two intersecting lines and the angles are
not adjacent. The two angles share a vertex. Such angles are equal in measure and can be described as
"equal" (in the UK or the USA) or "congruent" (in the USA).Read More About :- Associative Property of Addition Math.Edurite.comPage : 2/3