Sec 1-5

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Sec 1-5

• Concept Describe Angle Pair Relationships
• Objective Given a pair of angles, use special
  angle relationships to find angle measures.

2
Example 1

• The Alamillo Bridge in Seville, Spain, was
  designed by Santiago Calatrava. In the bridge,
  mlt158 and mlt224. Find the supplements of
  both lt1 and lt2

Suppl of lt1. 180-58 122
Suppl of lt2 180 24 156
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Example 2
Find the supplement and complement of each angle
A. 38 B. 172
A. Comp 52 Suppl 142 B. Comp none
Suppl 8
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Example 3 Find the measure of each angle
ltP and ltZ are complementary. mltP 8x - 7 and
mltZ x -11
Make an equation
mltP mltZ 90 8x-7 x-11 90 9x -18 90
18 18 9x 108 X12
mltP 8(12)-7 mltP 89 MltZ (12)-11 1
Now find each angle measure
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Example 4 Find the measure of each angle
ltP and ltZ are Supplementary. mltP 8x 100
and mltZ 2x50
Make an equation
mltP mltZ 180 8x100 2x50 180 10x150
180 -150 -150 10x 30 X3
mltP 8(3)100 mltP 124 MltZ 2(3)50
56
Now find each angle measure
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Example 5
Use the diagram to answer the following questions
1. Are lt1 and lt2 a linear pair? Yes 2. Are lt4
and lt5 a linear pair? NO 3. Are lt5 and lt3
Vertical angles? NO 4. Are lt1 and lt3 vertical
lts? YES
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Example 6
lt2 60.Find the measure of the other angles
mlt1 60 mlt2 60 mlt3 120 mlt4 120
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Example 7

• Find the measure of mltDEG and mltGEF

(7x-3) (12x-7) 180 19x-10 180 19x190 X10
7(10)-3 67 12(10)-7 113
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Example 8Find the measure of each angle

• 4x15 5x30 180
• 9x45 180
• -45 -45
• 9x 135
• 9
• X15

Use Linear Pairs to make and equation
Substitute x to find the angles
4(15)15 75 5(15)30 105
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Example 8 cont.Find the measure of each angle
3y15 3y-15 180 6y 180 6 6 y 30
Use Linear Pairs to make and equation
Substitute y to find the angles
3(30)15 105 3(30)-15 75
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Today's Work
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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
2 angles are adjacent if they share a common
vertex
ltDOS and ltSOG are adjacent angles
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Vertical Angles

• 2 angles are vertical angles if their sides form
  two pairs of opposite rays

lt1 and lt3 are vertical angles lt2 and lt4 are
vertical angles
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Linear Pair

• 2 adjacent angles are a linear pair if their
  non-common sides are opposite rays

lt5 and lt6 are a linear pair
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Complementary Angles
Two angles are Complementary if the sum of their
measures is 90
lt1 and lt2 are complementary
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Supplementary Angles
Two angles are Supplementary if the sum of their
measures is 180
lt 3 and lt4 are supplementary