Download Note Sheet 1-4

June 20, 2013
Geometry 1-4 Angle Measure
A ray is a part of a line. It has one endpoint, but it continues
forever in the other direction. Rays are named by their
endpoints, followed by any other point on the ray. The
endpoint MUST be named first.
C
ray AB or ray AC
B
A
AB or AC
Two rays are called opposite rays if they have the same
endpoint and they form a line.
K
J
L
An angle is formed by two noncollinear rays that share a
common endpoint. The two rays are called the sides of the
angle, and the common endpoint is called the vertex.
Name the sides and the vertex of this angle.
X
The sides of the angle are
ZX and ZY. The vertex is Z.
Z
Y
We name an angle by its vertex. If multiple angles share a
vertex, then we need to name a point on each side of the
angle. The angle above could be called⦛Z, or⦛XZY, or ⦛YZX.
An angle divides a plane into three parts: interior, exterior,
and on the angle.
A
J
interior
B
C
G
K
H
Angles that have the same measure are called congruent
angles. Similar to segments on a diagram, we mark
congruent angles with arcs.
1
2
⦛1 ~
= ⦛2
CE, CK
F
exterior
Angles are measured in degrees.
There are three main types of angles: acute (angles which
measure less than 90); right (angles which measure exactly
90); and obtuse (angles which measure greater than 90).
Name all angles that have B as a vertex.
⦛ABD, ⦛DBC
E Name the sides of⦛ECK.
D
Name a point on the interior of⦛JCF.
H
Any ray or line that cuts an angle into two congruent parts is
called an angle bisector.
M
L
K
J
N
Given: KM and KJ are opposite rays,
KN bisects⦛JKL. If m⦛JKN = 5y + 2
and m⦛JKL = 9y + 15, find m⦛JKL.
2m⦛JKN = m⦛JKL
2(5y + 2) = 9y + 15
10y + 4 = 9y + 15
y = 11
m⦛JKL = 9(11) + 15 = 114