Chapter 1.4 Notes: Measure and
Classify Angles
Goal: You will name, measure, and classify
angles.
• An angle consists of two different rays with the
same endpoint.
• The rays are the sides of the angle.
• The endpoint is the vertex of the angle.
• Name the angle above: _____, ______, ______
• ____________ is the vertex of the angle.
Ex.1: Name the three angles in the diagram.
Ex.2: Name the three angles in the diagram.
M
O
N
P
• Classifying Angles:
• Angles can be classified as acute, right, obtuse, and
straight.
• Acute angles have a measure greater than 0 and
less than 90.
• Right angles have a measure of 90.
• Obtuse angles have a measure greater than 90 and
less than 180.
• Straight angles have a measure of 180.
• Measuring Angles:
• A protractor can be used to approximate the
measure of an angle.
• An angle is measured in units called degrees (o).
• Postulate 3 Protractor Postulate:
Consider OB and a point A on one side of OB . The
rays of the form OA can be matched one to one
with the real numbers from 0 to 180.
The measure of AOB is equal to the absolute
value of the difference between the real numbers
for OA and OB .
A
O
B
EXAMPLE 3
Measure and classify angles
Use the diagram to find the measure of the indicated angle. Then
classify the angle.
a.
KHJ
b.
GHK
c.
GHJ
d.
SOLUTION
A protractor has an inner and an outer
scale. When you measure an angle,
check to see which scale to use.
GHL
• Postulate 4 Angle Addition Postulate:
If P is in the interior of RST , then the measure of
RST is equal to the sum of the measures of
RSP and PST .
If P is in the interior of RST , then
mRST  mRSP  mPST
Ex.4: Given that mLKN  145o , find mLKM and
mMKN .
Ex.5: If mXYZ  72o , find mXYW and
mZYW .
Ex.6: Given that KLM is a straight angle, find
mKLN and mNLM .
Ex.7: Given that EFG is a right angle, find
mEFH and mHFG .
• Congruent Angles:
• Two angles are congruent angles if they have the
same measure.
Angle measures ar equal
Angles are congruent
Ex.8: The photograph shows some of the angles
formed by the ropes in a trapeze apparatus. Identify
the congruent angles. If mDEG  157o , what is
mGKL?
Ex.9: Use the diagram below.
a. Identify all pairs of congruent angles.
o
o
o
m

TSR

121
m

PQR

130
b.
, mQRS  84 , and
.
Find the other angle measures in the diagram.
• An angle bisector is a ray that divides an angle into
two angles that are congruent.
Ex.10: In the diagram below, YW bisects XYZ , and
0
mXYW  18 . Find mXYZ.