1.6 Measuring
Angles
•
•
To Find the Measures of Angles
To Identify Special Angle Pairs
What is an Angle?
• An Angle (<) is
formed by two rays
that share the same
endpoint.
• The rays are the sides
of the angle.
• Here Ray BT and Ray
BQ meet at the
vertex of the angle,
which is B.
Naming an Angle…
We can name this Angle…
• By its vertex:
• < B (Angle B)
• By using three points:
• < TBQ (Angle TBQ)
• < QBT (Angle QBT)
• By a Number:
• < 1 (Angle One)
Naming Angles
• Name <1 in two other ways.
• < AEC
• <CEA
• Name <CED in two other ways.
•<2
• <DEC
• Can we name any of the angles <E? Why or Why
not?
Example 1A
a. Give Two other
names for <ABD.
b. Which 3 Angles
have D as their
Vertex?
Example 1B
c. Does <3 and <Z
name the same
Angle? Explain.
d. List all the angles
that have W as a
Vertex.
Classifying Angles by their
Measures
Classifying Angles by their
Measures
Congruent Angles…
• Angles with the same measures are Congruent Angles.
• In other words…
• If 𝑚 < 1 = 𝑚 < 2 then < 1 ≅ < 2
Angle Addition Postulate…
Ex 2: Using the Angle Addition
Postulate
a. What is m<TSW if
m<RST = 50 and
m<RSW = 125?
Ex 2B: Try one…
If m<DEG = 145, find m<GEF.
(Remember m<DEF=180
because it’s a Straight Angle)
Ex 3: Some More Algebra…
c.
In the figure, ray XP and ray XT are opposite rays and ray XQ
bisects <PXS. For each situation, find the value of x and the
measure of the indicated angle.
Ex 3: Some More Algebra…
d. Find m<RXS.
Identifying Angle Pairs…
Example 4
Tell whether each pair of angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
a. <AEB and <BED
b. <AEB and <BEC
c. <DEC and <AEB
Identifying Angle Pairs…
Identifying Angle Pairs…
Ex 5: Identify Angle Pairs
Ex 6: Find The Measure…
Find:
a) complement of <F
b) supplement of <F
Ex 7: Find x!
What can I assume from a
diagram?
If you are given a diagram, there are some ideas we can
conclude just by looking at it.
You can conclude that angles are:
• Adjacent
• Adjacent Supplementary
• Vertical
• Straight
What can’t I assume from a
Diagram?
Unless there are marks or symbols indicated in the
diagram, you cannot assume that:
• Angles or segments are congruent
• Angles are Right or 90 degrees
• Lines are Parallel or Perpendicular
Make Conclusions…
Ex 8: Can you make these
conclusions?
Closure…
• How are angles
classified?
• What are the special
Angle pairs?