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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.

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Example 1 The 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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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 ~~
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3 1 4 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

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4x+15 5x+30 3y + 15 3y -15 Use Linear Pairs to make and equation 4x+15 + 5x+30 = 180 9x+45 = 180 -45 -45 9x = 135 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+30 3y + 15 3y -15 Use Linear Pairs to make and equation 3y+15 + 3y-15 = 180 6y = 180 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

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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 Pair 2 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

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