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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 1 3) 180 Rule for Triangles Objective-To find missing angles and to solve word problems involving geometric figures. Some Strategies 1) Supplementary Angles 2) Complementary Angles 4) Vertical Angles 2:6 Word Problems Involving Geometric Figures

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 2 Supplementary Angles- Angles whose sum is 180. a b x 30 x + 30 = 180 - 30 x = 150 Find the value of x.

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 3 Find the supplement of the given angle. 1) 40 2) 18 3) 153 4) 65 5) 89 6) 23 7) 131 8) 118 140 162 27 115 91 157 49 62

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 4 Write a variable equation and solve. Find an angle whose supplement is 30 less than twice the angle. x2x - 30 x + (2x - 30) = 180 3x - 30 = 180 +30 3x = 210 x = 70 70

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 5 Complementary Angles - Angles whose sum is 90. a b x 40 x + 40 = 90 - 40 -40 x = 50

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 6 Find the complement of... 1) 20 2) 47 3) 100 4) the supplement of 150 70 43 No complement the complement of the supplement of 150 30the complement of= 60

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 7 Write a variable equation and solve. Find an angle whose complement is 20 more than three times the angle. x 3x + 20 x + 3x + 20 = 90 4x + 20 = 90 - 20 -20 4x = 70 4 x = 17.5

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 8 180 Rule for Triangles - the sum of the interior angles of any triangle is always 180. a b c 40 80 x 40 + 80 + x = 180 120 + x = 180 x = 60

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 9 Find each angle below. y +14 y - 20 2y - 10 (y + 14) + (2y - 10) + (y - 20) = 180 4y - 16 = 180 +16 4y = 196 y = 49 y + 14 = 63 2y - 10 = 88 y - 20 = 29 180

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 10 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal.

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 11 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal.

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 12 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal. Find the missing angles a, b and c. 25 a b c 155

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 13 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal. Find the missing angles a, b and c. 25 a b c 155

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 14 Find the missing angle. 40132 x 48 x = 180 - 40 - 48 x = 92

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 15 Find the missing angle. 119 x 124 61 56 x = 180 - 61 - 56 x = 63

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 16 Use a variable equation to solve. 1) The length of a rectangle is 5 less than 3 times its width. If the perimeter is 30 ft., find its dimensions. Let x = width 3x - 5 = length x 3x - 5 2(x) + 2(3x - 5) = 30 2x + 6x - 10 = 30 +10 8x = 40 8 x = 5 = 5 = 10

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 17 2) An angle is 6 degrees less than 3 times its complement. Find the angle. Let x = the complement x 3x - 6 = the angle x + (3x - 6) = 90 (3x - 6) 4x - 6 = 90 +6 4x = 96 4 x = 24 = 24 = 3(24) - 6 = 66

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 18 3) The largest angle in a triangle is four times the smallest. The third angle is 5 more than twice the smallest. Find each angle. Let n = the smallest angle 2n + 5 = the middle angle 4n = the largest angle n 2n + 5 4n n + (2n + 5) + 4n = 180 7n + 5 = 180 -5 7n = 175 7 n = 25 = 25 = 55 = 100

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Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 19 4) The lengths of the sides of a triangle are consecutive even integers. If the perimeter is 24 inches, find the length of each side. Let x = 1st side x + 2 = 2nd side x + 4 = 3rd side x x + 2 x + 4 x + (x + 2) + (x + 4) = 24 3x + 6 = 24 -6 3x = 18 3 x = 6 = 6 in. = 8 in. = 10 in.

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