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Notes on Angle Relationships
Angle:
Definition: A shape formed by two lines or rays diverging from a common point (the
vertex). In easier terms: is a figure that is formed from two rays that extend from a
common point called the vertex.
Vertex
Angle B is the name of the angle
Angle ABC is also the name of the angle
B is the vertex
The vertex is the common point at which the two lines or rays are joined.
Point B in the figure above is the vertex of the angle ∠ABC.
Legs
The legs (sides) of an angle are the two lines that make it up. In the figure
above, the lines AB and BC are the legs of the angle ∠ABC.
Interior
The interior of an angle is the space in the 'jaws' of the angle extending
out to infinity.
Exterior
All the space on the plane that is not the interior.
 The symbol m∠ is used to denote the measure of an angle.
 The unit of measure for angles is in degrees.
 There are 360 degrees around a circle.
Type of angles
Acute angle
Right angle
Obtuse angle
Straight angle
Reflex angle
description
an angle that is less than 90°
an angle that is 90° (exactly)
an angle that is greater than 90°
but less than 180°
an angle that is 180° (exactly)
an angle that is greater than
180°
In One Diagram
This diagram might make it easier to remember:
Also: Acute, Obtuse and Reflex are in alphabetical order.
Be Careful What You Measure
This is an Obtuse Angle.And this is a Reflex Angle.
But the lines are the same ... so when naming the angles make sure
that you know which angle is being asked for!
The measure of an angle is the smallest amount of rotation about the vertex from
one ray to the other, measured in degrees. According to this definition, the
measure of an angle can be any value between 0° and 180°. The largest amount of
rotation less than 360° between the two rays is called the reflex measure of an
angle.
Angle Relationships:
Supplementary angles:
These two angles (140° and
40°) are Supplementary
Angles, because they add
up to 180°.
Notice that together they
make a straight angle.
But the angles don't have
to be together.
These two are
supplementary because
60° + 120° = 180°
Complementary:
Two Angles are Complementary if they add up to 90 degrees (a Right Angle).
These two angles (40° and 50°) are
Complementary Angles, because they
add up to 90°.
Notice that together they make a right
angle.
But the angles don't have to be
together.
These two are complementary because
27° + 63° = 90°
Right Angled Triangle
In a right angled triangle, the two nonright angles are complementary,
because in a triangle the three angles
add to 180°, and 90° has already been
taken by the right angle.
Complementary vs Supplementary.
 "C" of Complementary stands for "Corner"
(a Right Angle), and
 "S" of Supplementary stands for "Straight" (180 degrees is a straight line)
Adjacent angles
Definition: two coplanar angles with a common side, a common vertex, and no
common interior points.
In other words:Two angles that share a common side and a common vertex, but do
not overlap
Adjacent angles: angle 1 and 2 are adjacent
 They may or may not be supplementary
Linear Pairs
Definition: Two angles that are adjacent (share a leg) and supplementary (add up
to 180°)
Angle 3 and 4 are linear pairs
Vertical Angles
Definition: A pair of non-adjacent angles formed by the intersection of two straight
lines. They are congruent.
In other words: Vertical angles are the angles that are opposite each other when
two lines intersect. (Technically, these two lines need to be
on the same plane)
In the picture on the left,
1 and
2 are vertical
angles. Likewise,
A and
B are vertical. Vertical
angles are always congruent (equal).
Angle bisector
Definition: it is a line or ray passing through the vertex of the angle that cuts it into
two equal smaller angles.
In other words: A line which cuts an angle into two equal halves
In general 'to bisect' something means to cut it into two equal parts. The 'bisector'
is the thing doing the cutting.