LESSON How can you use angle relationships to solve problems? Angle Relationships 9.1.
Sec 1-5 Concept: Describe Angle Pair Relationships Objective: Given a pair of angles, use special...
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Transcript of Sec 1-5 Concept: Describe Angle Pair Relationships Objective: Given a pair of angles, use special...
![Page 1: Sec 1-5 Concept: Describe Angle Pair Relationships Objective: Given a pair of angles, use special angle relationships to find angle measures.](https://reader035.fdocuments.net/reader035/viewer/2022062511/5515bcdf550346a1418b6402/html5/thumbnails/1.jpg)
Sec 1-5Sec 1-5Sec 1-5Sec 1-5Concept: Describe Angle Pair Concept: Describe Angle Pair
RelationshipsRelationshipsObjective: Given a pair of angles, use Objective: Given a pair of angles, use
special angle relationships to find angle special angle relationships to find angle measures.measures.
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Example 1The Alamillo Bridge in Seville, Spain, was designed by
Santiago Calatrava. In the bridge, m<1=58° and m<2=24°. Find the supplements of both <1 and <2
Suppl of <1. 180-58 =
122
Suppl of <2: 180 – 24 =
156
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A. 38°
B. 172°
A. Comp: 52° Suppl: 142°
B. Comp: none Suppl: 8°
Find the supplement and complement of each angle
Example 2:
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<P and <Z are complementary.
m<P = 8x - 7 and m<Z = x -11
m<P + m<Z = 90
8x-7 + x-11 = 90
9x -18 = 90
+18 +18
9x = 108
X=12
Make an
equation
Now find
each angle
measure
m<P = 8(12)-7
m<P = 89°
M<Z= (12)-11
= 1
Example 3: Find the measure of each angle
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<P and <Z are Supplementary.
m<P = 8x + 100 and m<Z = 2x+50
m<P + m<Z = 180
8x+100 + 2x+50 = 180
10x+150 = 180
-150 -150
10x = 30
X=3
Make an
equation
Now find
each angle
measure
m<P = 8(3)+100
m<P = 124°
M<Z= 2(3)+50
= 56°
Example 4: Find the measure of each angle
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2
1 5
4
3
1. Are <1 and <2 a linear pair?
Yes
2. Are <4 and <5 a linear pair?
NO
3. Are <5 and <3 Vertical angles?
NO
4. Are <1 and <3 vertical <‘s?
YES
Use the diagram to answer the following questions
Example 5
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3
14
2
m<1= 60
m<2 = 60
m<3 = 120
m<4 = 120
<2 = 60°.Find the measure of the other angles
Example 6
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Example 7 :Find the measure of m<DEG and m<GEF
(7x-3) + (12x-7) = 180
19x-10 = 180
19x=190
X=10
7(10)-3 = 67
12(10)-7 =113
(7x-3)۫ (12x-7)۫
D E F
G
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4x+15
5x+303y + 15
3y -15
Use Linear Pairs to make
and equation
4x+15 + 5x+30 = 180
9x+45 = 180
-45 -45
9x = 135
9 9
X=15
Substitute x to find the angles
4(15)+15 =
75
5(15)+30 =
105
Example 8:Find the measure of each angle
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4x+15
5x+303y + 15
3y -15
Use Linear Pairs to make
and equation
3y+15 + 3y-15 = 180
6y = 180
6 6
y = 30
Substitute y to find the angles
3(30)+15 =
105
3(30)-15 =
75
Example 8 cont.:Find the measure of each angle
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Additional Slides:
• The following are Terms that you can move and place where you like:
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Adjacent Angles
D
O
S
G
2 angles are adjacent if they share a common vertex
<DOS and <SOG are
adjacent angles
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Vertical Angles 2 angles are vertical angles if their sides form two pairs of opposite rays
1 2
3 4
<1 and <3 are vertical angles
<2 and <4 are vertical angles
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Linear Pair2 adjacent angles are a linear pair if their non-common sides are opposite rays
5 6<5 and <6 are a
linear pair
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Complementary Angles
Two angles are Complementary if the sum of their measures is 90°
<1 and <2 are complementary
30°
60°
1 2
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Supplementary Angles
Two angles are Supplementary if the sum of their measures is 180°
130°50°
3 4
< 3 and <4 are supplementary