1.4 Angles
and Their
Measures
Geometry
Mrs. Blanco
Standard/Objectives:
Objectives:
• Use angle postulates
• Classify angles as acute, right, obtuse, or
straight.
Using Angle Postulates
• An angle consists of two
different rays that have
the same initial point.
The rays are the sides of
the angle. The initial
point is the vertex of the
angle.
• The angle that has sides
AB and AC.
• Angles name:by BAC,
CAB, A. The point A
is the vertex of the
angle.
Ex.1: Naming Angles
• Name the angles in
the figure:
SOLUTION:
There are three
different angles.
BE CAREFUL:
• PQS or SQP
You should not name any of
• SQR or RQS
these angles as Q because
• PQR or RQP
all three angles have Q as their
vertex. The name Q would
not distinguish one angle from
the others.
Note:
• The measure of A is denoted by mA.
• mBAC = 50° or mA= 50°
BAC and DEF each have a
measure of 50°, so they are congruent.
MEASURES ARE EQUAL
ANGLES ARE CONGRUENT
mBAC = mDEF
BAC  DEF
“is equal to”
“is congruent to”
Interior/Exterior
• A point is in the
interior of an angle if
it is between points
that lie on each side
of the angle.
• A point is in the
exterior of an angle if
it is not on the angle
or in its interior.
Postulate 4: Angle Addition
Postulate
• If P is in the interior
of RST, then
mRSP + mPST =
mRST
Ex. 2: Calculating Angle
Measures
• VISION. Each eye of
a horse wearing
blinkers has an angle
of vision that
measures 100°. The
angle of vision that is
seen by both eyes
measures 60°.
• Find the angle of
vision seen by the
left eye alone.
Classifying Angles
Ex. 3: Classifying Angles in a
Coordinate Plane
•
Plot the points A(-2,4), B(3,5), C(6,-1),
D(3,-4), E(-3,-3) and F(3,-1).
• Use protractor to measure and classify
the following angles as acute, right,
obtuse, or straight.
a. AFD
b. AFE
c. BFD
d. BFC
Need Graph Paper
Solution:
Ex. 4: Adjacent Angles
Two angles are adjacent angles if they share a
common vertex and side, but have no common
interior points.
PQS and SQR are adjacent
Closure Question:
• Describe how angles are classified.
Angles are classified according to their
measure.
• Acute--less than 90° are acute.
• Right-- measuring 90°
• Obtuse-- between 90° and 180°
• Straight--exactly 180°
Extra Example—Angle Addition