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1-3 Measuring and Constructing Angles
Objectives
Name and classify angles.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Vocabulary
angle
vertex
interior of an angle
exterior of an angle
measure
degree
acute angle
Holt McDougal Geometry
right angle
obtuse angle
straight angle
congruent angles
angle bisector
1-3 Measuring and Constructing Angles
__________ – a figure formed by two rays, or
sides, with a common endpoint called the
__________ (plural: __________ ).
ray
vertex
ray
You
•by
•by
•by
can name an angle several ways:
its vertex,
a point on each ray and the vertex, or
a number.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
____________________– the set of all points between
the sides of the angle.
____________________ – the set of all points outside
the angle.
Angle Name
__________, __________ ,
__________ , or __________
You cannot name an angle just by its vertex if the
point is the vertex of more than one angle. In this
case, you must use all three points to name the
angle, and the middle point is always the vertex.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 1
Write the different ways
you can name the angles
in the diagram.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 2
Find the measure of each angle. Then classify
each as acute, right, or obtuse.
A. WXV
B. ZXW
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 2 Continued
Use the diagram to find the measure of each
angle. Then classify each as acute, right, or
obtuse.
C. BOA
D. DOB
E. EOC
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
____________________ are angles that have the same
measure.
mABC = mDEF, so ABC  DEF.
This is read as “angle ABC is congruent to angle DEF.”
__________ are used to show that the two angles are
congruent.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 3a: Using the Angle Addition Postulate
mDEG = 115°, and mDEF = 48°. Find mFEG
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 3b
mXWZ = 121° and mXWY = 59°. Find mYWZ.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
An _______________is a ray that divides an angle
into two congruent angles.
JK bisects LJM; thus LJK  KJM.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 4a
KM bisects JKL, mJKM = (4x + 6)°, and
mMKL = (7x – 12)°. Find mJKM.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 4b
Find the measure of each angle.
QS bisects PQR, mPQS = (5y – 1)°, and
mPQR = (8y + 12)°. Find mPQS.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 4c
Find the measure of each angle.
JK bisects LJM, mLJK = (-10x + 3)°, and
mKJM = (–x + 21)°. Find mLJM.
Holt McDougal Geometry