Transcript Angles

Angles
Definition
An angle is a figure
formed by 2 rays with
a common endpoint.
•
Parts of an Angle
Sides are the 2 rays
that form the angle.
PS and PQ are sides
Vertex is the common
endpoint for both rays.
P is the vertex
Naming an Angle



Use the vertex
<B
Use 3 letters with the
vertex in the center
<ABC or <CBA
Use a number inside
the angle
<1
A
•
B
•
1
•
C
Types of Angles

Acute angle measures between
0° and 90°

Right angle measures 90°

Obtuse angle measures
between 90° and 180°

Straight angle measures 180°
Protractor Postulate
Given ray AB and a
number r between 0 and 180,
there is exactly one ray with
endpoint A, extending on
each side of AB, such that the
measure of the angle
formed is r.
•
A
r
°
r
°
•B
Angle Addition Postulate
If D is in the interior of <ABC, then
m<ABD + m<DBC = m<ABC
35°
18°
m<ABC = 35° +
18°
m<ABC = 53°
Congruent Angles
Congruent angles are
angles that have the
same measure.
1
2
Ð1 @ Ð2 (angles are congruent )
m Ð1 = m Ð2 (measures are equal )
Pairs of Angles

Adjacent angles are coplanar
and share a side and a vertex,
but do not overlap

Vertical angles are 2
nonadjacent angles formed by 2
intersecting lines

Linear pair of angles are 2
adjacent angles that share a side
and the other 2 sides are
opposite rays
Pairs of Angles

Complementary angles are 2
angles whose sum is 90°

Supplementary angles are 2
angles whose sum is 180°

Note: Complementary & Supplementary
angles can be adjacent, but do not have
to be adjacent.
Angle Relationships
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
Linear Pair Postulate
Two angles that form a linear
pair are supplementary
Vertical Angle Theorem
Vertical angles are congruent
1
2
m<1 + m<2 = 180°
3
4
m<3 = m<4