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Objective
Identify and apply angle relationships
Vocabulary
Vertical angles
Opposite angles formed by the intersection
of two lines
1
Vocabulary
Congruent angles
Angles that have the same measure
Vocabulary
Supplementary angles
Two angles that have the sum of their
measures as 1800
Vocabulary
Complementary angles
Two angles are complementary if the sum
of their measures is 900
Math Symbols
Is congruent to

Example 1 Classify Angles
Example 2 Classify Angles
Example 3 Find a Missing Angle Measure
Example 4 Use Angles to Solve A Problem
Classify the pair of angles as complementary,
supplementary, or neither
1280 + 520
1800
Answer:.
Supplementary
Add the two angle measurements
together
Meets the definition of
supplementary angles
1/4
Classify the pair of angles as complementary,
supplementary, or neither
Answer: complementary
1/4
Classify the pair of angles as complementary,
supplementary, or neither
Right angle = 900
Answer:
Complementary
x and y form a right angle
Meets the definition of
complementary angles
2/4
Classify the pair of angles as complementary,
supplementary, or neither
Answer: supplementary
2/4
Angles PQS and RQS are supplementary.
If mPQS 56, find mRQS.
mPQS + mRQS = 1800
560
mPQS is 560
PQS and RQS are supplementary
Remember:
Supplementary angles = 1800
3/4
Angles PQS and RQS are supplementary.
If mPQS 56, find mRQS.
mPQS + mRQS = 1800
560
+ mRQS =
1800
560
Replace mPQS with 560
Bring down + mRQS = 1800
Solve for the unknown mRQS
3/4
Angles PQS and RQS are supplementary.
If mPQS 56, find mRQS.
mPQS + mRQS = 1800
560 + mRQS = 1800
560 - 560
Ask “what is being done to the
variable?”
The variable (mRQS) is
being added by 560
Do the inverse on both sides
of the equal sign
Bring down 560
Subtract 560
3/4
Angles PQS and RQS are supplementary.
If mPQS 56, find mRQS.
mPQS + mRQS = 1800
560 + mRQS = 1800
Bring down + mRQS = 1800
Subtract 560
560 - 560 + mRQS = 1800 - 560
00 + mRQS = 1240
Combine “like” terms
Bring down + mRQS =
Combine “like” terms
3/4
Angles PQS and RQS are supplementary.
If mPQS 56, find mRQS.
mPQS + mRQS = 1800
560 + mRQS = 1800
Use the Identify Property to
add 00 + mRQS
560 - 560 + mRQS = 1800 - 560
00 + mRQS = 1240
Bring down 1240
Answer:
mRQS = 1240
3/4
Angles MNP and KNP are complementary.
If mMNP 23, find mKNP.
Answer: m KNP = 67
3/4
GEOMETRY The rectangle shown is divided by a diagonal.
Find the value of x.
x0 + 700 = 900
The angle that x0 and 700 make
is a right angle
A right angle = 900
Write an equation
Solve for the unknown
4/4
GEOMETRY The rectangle shown is divided by a diagonal.
Find the value of x.
Ask “what is being done to the
x0 + 700 = 900
variable?”
X0 + 700 - 700
The variable is being added
by 700
Do the inverse on both sides
of the equal sign
Bring down x0 + 700
Subtract 700
4/4
GEOMETRY The rectangle shown is divided by a diagonal.
Find the value of x.
Bring down = 900
x0 + 700 = 900
Subtract 700
x0 + 700 - 700 = 900 - 700
Bring down x0 +
x0 + 00 = 200
Combine “like” terms
Answer:
x0 = 200
Bring down =
Combine “like” terms
Use the Identify Property to
add x + 00
Bring down 200
4/4
*
GRAPHING In the circle graph shown below, find the
value of x.
Answer: x = 620
4/4
Assignment
Lesson 10:3
Angle Relationship
3 - 21 All