holt ca course 1 9-4 finding angle measures warm up warm up california standards california...
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Holt CA Course 1
9-4 Finding Angle Measures
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California StandardsCalifornia Standards
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Holt CA Course 1
9-4 Finding Angle Measures
Warm UpTell whether the given angles are vertical, complementary, or supplementary.
1. QXT and QXR
2. QXR and TXS
3. PXQ and QXR
4. PXQ and PXS
5. TXS and SXR
supplementary
vertical
complementary
supplementary
supplementary
Holt CA Course 1
9-4 Finding Angle Measures
MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.Also covered: AF1.1, MG2.1
California Standards
Holt CA Course 1
9-4 Finding Angle Measures
Objective:Objective: You will learn You will learn how to (YWLHT) use angle how to (YWLHT) use angle relationships to find angle relationships to find angle measures.measures.
Holt CA Course 1
9-4 Finding Angle Measures
Example 1: Finding an Unknown Angle Measure
Find each unknown angle measure.
Since the angles are complementary, the sum of the angle measures is 90°.
aa
71°
A. The angles are complementary.
Holt CA Course 1
9-4 Finding Angle Measures
Example 1: Finding an Unknown Angle Measure
Find each unknown angle measure.
71° + maa = 90°–71° –71°
maa = 19°
Since the angles are complementary, the sum of the angle measures is 90°.
aa
71°
A. The angles are complementary.
Subtract 71° from both sides.
Holt CA Course 1
9-4 Finding Angle Measures
aa125°
B. The angles are supplementary.
Since the angles are supplementary, the sum of the angle measures is 180°.
Example 2: Finding an Unknown Angle Measure
Find each unknown angle measure.
Holt CA Course 1
9-4 Finding Angle Measures
125° + maa = 180°–125° –125°
maa = 55°
Subtract 125° from both sides.
aa125°
B. The angles are supplementary.
Since the angles are supplementary, the sum of the angle measures is 180°.
Example 2: Finding an Unknown Angle Measure
Find each unknown angle measure.
Holt CA Course 1
9-4 Finding Angle Measures
aa 82°
C. The angles are vertical angles.
Example 3: Finding an Unknown Angle Measure
Find each unknown angle measure.
Since the angles are vertical angles, the angles are congruent.
Holt CA Course 1
9-4 Finding Angle Measures
maa = 82° Congruent angles have the same measure.
aa 82°
C. The angles are vertical angles.
Example 3: Finding an Unknown Angle Measure
Find each unknown angle measure.
Since the angles are vertical angles, the angles are congruent.
Holt CA Course 1
9-4 Finding Angle Measures
The sum of the measures is 180°.
D. BEA CED; mAED = 180°aa31°E
CB
DA
Example 4: Finding an Unknown Angle Measure
Find each unknown angle measure.
Holt CA Course 1
9-4 Finding Angle Measures
31° + maa + 31° = 180°
–62° –62° 62° + maa = 180°
The sum of the measures is 180°.
D. BEA CED; mAED = 180°
maa = 118°
aa31°E
CB
DA
Example 4: Finding an Unknown Angle Measure
Find each unknown angle measure.
Holt CA Course 1
9-4 Finding Angle MeasuresCheck It Out! Example 5
Find each unknown angle measure.
65° + md = 90°–65° –65°
md = 25°
Subtract 65° from both sides.
d
65°
A. The angles are complementary.
Since the angles are complementary, the sum of the angle measures is 90°.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle MeasuresCheck It Out! Example 6
Find each unknown angle measure.
145° + ms = 180°–145° –145°
ms = 35°Subtract 145° from both sides.
s145°
B. The angles are supplementary.
Since the angles are supplementary, the sum of the angle measures is 180°.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle MeasuresCheck It Out! Example 7
Find each unknown angle measure.
mt = 32° Congruent angles have the same measure.
t
32°
C. The angles are vertical angles.
Since the angles are vertical angles, the angles are congruent.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
25° + b + 25° = 180°
–50° –50°
50° + b = 180°
The sum of the measures is 180°.
D. WZV XZY; mVZY = 180°
b = 130°
Check It Out! Example 8
Find each unknown angle measure.
b25°Z
XW
YV
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
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Holt CA Course 1
9-4 Finding Angle Measures
–27° –27°27° + c = 90° The sum of the measures is 90°.
c = 63°
Subtract 27° from both sides.
Example 9: Application
Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.
Step 1: The angles labeled c and 27° are complementary. To find c, use properties of complementary angles.
Holt CA Course 1
9-4 Finding Angle Measures
–151° –151°
151° + a = 180° The sum of the measures is 180°.
a = 29°
Subtract 151° from both sides.
Example 9 Continued
Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.
Step 2: The angles labeled a and 151° are supplementary. To find a, use properties of supplementary angles.
Holt CA Course 1
9-4 Finding Angle Measures
b = 27° Vertical angles are congruent.
Example 9 Continued
Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.
Step 3: The angles labeled b and 27° are vertical angles. To find b, use properties of vertical angles.
Holt CA Course 1
9-4 Finding Angle Measures
–22° –22°22° + z = 90°
z = 68°
Check It Out! Example 10
Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.
x 165°
22°z
y
Step 1: The angles labeled z and 22° are complementary. To find z, use properties of complementary angles.
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
–165° –165°
165° + x = 180°
x = 15°
Check It Out! Example 10 Continued
Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.
Step 2: The angles labeled x and 165° are supplementary. To find x, use properties of supplementary angles.
x 165°
22°z
y
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
y = 22°
Check It Out! Example 10 Continued
Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.
Step 3: The angles labeled y and 22° are vertical angles. To find y, use properties of vertical angles.
x 165°
22°z
y
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...
Holt CA Course 1
9-4 Finding Angle Measures
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LearningLearning
On-Line On-Line TutoringTutoring
Geo-match-tryGeo-match-try
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Holt CA Course 1
9-4 Finding Angle Measures
Lesson Quiz: Part I
Find each unknown angle measure.
1. The angles are vertical angles.
2. The angles are supplementary.
d = 130°
x = 45°
Holt CA Course 1
9-4 Finding Angle MeasuresLesson Quiz: Part II
p = 78°
3. KNL = LNM; mJNM = 180°
4. Use the information in the diagram to find
the unknown angle measures a, b, and c.
Show your work.
@
a = 147°, b = 123°, c = 19°