Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Tell 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
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Additional Example 1 Finding an Unknown Angle
Measure Find each unknown angle measure.
A. The angles are complementary.
Since the angles are complementary, the sum of
the angle measures is 90.
71 m?1 90
Subtract 71 from both sides.
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71 71
m?1 19
71
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Additional Example 1 Finding an Unknown Angle
Measure Find each unknown angle measure.
B. The angles are supplementary.
Since the angles are supplementary, the sum of
the angle measures is 180.
125 m?2 180
Subtract 125 from both sides.
125 125
m?2 55
125
2
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Additional Example 1 Finding an Unknown Angle
Measure Find each unknown angle measure.
C. The angles are vertical angles.
Since the angles are vertical angles, the angles
are congruent.
Congruent angles have the same measure.
m?3 82
3
82
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Additional Example 2 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.
The sum of the measures is 90.
27 c 90
27 27
Subtract 27 from both sides.
c 63
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Additional Example 2 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.
The sum of the measures is 180.
151 a 180
151 151
Subtract 151 from both sides.
a 29
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Additional Example 2 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.
b 27
Vertical angles are congruent.
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Check It Out! Example 1 Find each unknown angle
measure.
A. The angles are complementary.
Since the angles are complementary, the sum of
the angle measures is 90.
65 m?d 90
d
Subtract 65 from both sides.
65 65
m?d 25
65
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Lesson Quiz Part I
Find each unknown angle measure. 1. The angles
are vertical angles. 2. The angles are
supplementary.
d 130
x 45
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Lesson Quiz Part II
3. ?KNL ?LNM m?JNM 180 4. Use the
information in the diagram to find the unknown
angle measures a, b, and c. Show your work.

p 78
a 147, b 123, c 19
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Check It Out! Example 1 Find each unknown angle
measure.
B. The angles are supplementary.
Since the angles are supplementary, the sum of
the angle measures is 180.
145 m?s 180
Subtract 145 from both sides.
145 145
m?s 35
145
s
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Check It Out! Example 1 Find each unknown angle
measure.
C. The angles are vertical angles.
Since the angles are vertical angles, the angles
are congruent.
Congruent angles have the same measure.
m?t 32
t
32
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