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5-1 Angle Relationships
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-1 Angle Relationships
Warm Up
Solve.
1. x + 30 = 90
x = 60
2. 103 + x = 180 x = 77
3. 32 + x = 180
x = 148
4. 90 = 61 + x
x = 29
5. x + 20 = 90
x = 70
5-1 Angle Relationships
Problem of the Day
Mrs. Meyer’s class is having a pizza party.
Half the class wants pepperoni on the
pizza, 1 of the class wants sausage on the
3
pizza, and the rest want only cheese on the
pizza. What fraction of Mrs. Meyer’s class
wants just cheese on the pizza?
1
6
5-1 Angle Relationships
Learn to classify angles and find their
measures.
5-1 Angle Relationships
Vocabulary
angle
adjacent angles
right angle
supplementary angles
acute angle
complementary angles
obtuse angle
straight angle
vertical angles
congruent angles
5-1 Angle Relationships
An angle () is formed by two rays, or
sides, with a common endpoint called
the vertex. You can name an angle
several ways: by its vertex, by its
vertex and a point on each ray, or by a
number. When three points are used,
the middle point must be the vertex.
5-1 Angle Relationships
5-1 Angle Relationships
Additional Example 1: Classifying Angles
Use the diagram to name each figure.
A. two acute angles
TQP, RQS mTQP = 43°; mRQS = 47°
B. two obtuse angles
SQP, RQT
mSQP= 133°; mRQT = 137°
5-1 Angle Relationships
Additional Example 1: Classifying Angles
Use the diagram to name each figure.
C. a pair of complementary angles
TQP, RQS mTQP + mRQS = 43° + 47° = 90
B. two pairs of supplementary angles
TQP, TQR mTQP + mTQR = 43° + 137° = 180
SQP, SQR mSQP + mSQR = 133° + 47° = 180
5-1 Angle Relationships
Check It Out: Example 1
Use the diagram to name each figure.
A. two acute angles
AEB, CED mAEB = 15°; mCED = 75°
B. two obtuse angles
AEC, BED
mAEC= 105°; mBED = 165°
5-1 Angle Relationships
Check It Out: Example 1
Use the diagram to name each figure.
C. a pair of complementary angles
AEB, CED mAEB + mCED= 15° + 75° = 90
D. a pair of supplementary angles
CED, AEC
mCED + mAEC = 75° + 105° = 180
5-1 Angle Relationships
Additional Example 2A: Finding Angle Measures
Use the diagram to find each angle measure.
If m1 = 37°, find m2.
m1 + m2 = 180°
1 and 2 are supplementary.
37° + m2= 180°
Substitute 37 for m1.
Subtract 37 from both sides.
–37°
–37°
m2 = 143°
5-1 Angle Relationships
Additional Example 2B: Finding Angle Measures
Use the diagram to find each angle measure.
Find m3 = 37°.
m2 + m3 = 180°
2 and 3 are supplementary.
143° + m3 = 180°
Substitute 143 for m2.
Subtract 143 from both sides.
–143°
–143°
m3 = 37°
5-1 Angle Relationships
Check It Out: Example 2
Use the diagram to find each
angle measure.
If m1 = 42°, find m2.
m1 + m2 = 180°
1 and 2 are supplementary.
42° + m2= 180°
Substitute 42 for m1.
Subtract 42 from both sides.
–42°
–42°
m2 = 138°
5-1 Angle Relationships
Adjacent angles have a common
vertex and a common side, but no
common interior points. Angles 1 and
2 in the diagram are adjacent angles.
Congruent angles have the same
measure.
Vertical angles are the nonadjacent
angles formed by two intersecting
lines. Angles 2 and 4 are vertical
angles. Vertical angles are congruent.
5-1 Angle Relationships
Additional Example 3: Application
A traffic engineer designed a
section of roadway where three
streets intersect. Based on the
diagram, what is the measure of
DBE.
Step 1: Find mCBD.
ABF  CBD
mABF = mCBD
mCBD = 26
Vertical angles are congruent.
Congruent angles have the
same measure.
Substitute 26 for mCBD.
5-1 Angle Relationships
Additional Example 3 Continued
A traffic engineer designed a
section of roadway where three
streets intersect. Based on the
diagram, what is the measure of
DBE.
Step 2: Find mDBE.
mCBD + mDEB = 90° The angles are complementary.
26 + mDEB = 90° Substitute 26 for mCBD.
–26°
–26° Subtract 26 from both sides.
mDEB = 64°
5-1 Angle Relationships
Check It Out: Example 3
A traffic engineer designed a
section of roadway where three
streets intersect. Based on the
diagram, what is the measure of
DBE.
Step 1: Find mCBD.
ABF  CBD
mABF = mCBD
mCBD = 19
19
Vertical angles are congruent.
Congruent angles have the
same measure.
Substitute 19 for mCBD.
5-1 Angle Relationships
Check It Out: Example 3 Continued
A traffic engineer designed a
section of roadway where three
streets intersect. Based on the
diagram, what is the measure of
DBE.
Step 2: Find mDBE.
19
mCBD + mDEB = 90° The angles are complementary.
19 + mDEB = 90° Substitute 19 for mCBD.
–19°
–19° Subtract 19 from both sides.
mDEB = 71°
5-1 Angle Relationships
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
5-1 Angle Relationships
Lesson Quiz
Use the diagram to name each figure or find
each angle measure.
1. a right angle
Possible answer: CGD
2. two acute angles
Possible answer: 1, 2
3. pair of complementary angles
Possible answer: 3, 4
4. If m1 = 47°, then find m 3.
47°
5. Find m4.
43°
5-1 Angle Relationships
Lesson Quiz for Student Response Systems
1. If m1 = 42°, then find m 3.
A. 3°
B. 42°
C. 48°
D. 90°
5-1 Angle Relationships
Lesson Quiz for Student Response Systems
2. Name a pair of complementary angles.
A. CGD
B. AGF
C. AGB, BGC
D. CGD, DGF
5-1 Angle Relationships
Lesson Quiz for Student Response Systems
3. Find mCGD.
A. 3°
B. 42°
C. 90°
D. 180°