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Angles, Angles of Triangles and Parallel Lines

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Angles Angles are produced when two or more lines meet or cross.

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Angles When working out the size of angles always give reasons for your answers This is important as the examiners give marks for correct reasons.

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Types of Angles And 4 right angles make 360 o A right angle is exactly 90° So 2 right angles make 180 o – a straight line – a complete turn

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Acute angle This is any size angle LESS than 90° Obtuse angle This is an angle between 90° and 180° Reflex angle This is an angle greater than 180° Types of Angles

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Angle Properties For two intersecting lines Vertically opposite angles are equal Adjacent angles add up to 180° a + b = 180º a a b b

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Angle Properties Angles at a Point All the angles add up to 360°

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Angle Properties Complimentary angles add up to 90º Supplementary angles add up to 180º The angles on a straight line add up to 180 o 40 o 50 o 70 o 30 o 80 o The missing angle is 50 o The missing angle is 80 o

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Find the missing angles 1. 2. 3. 4. 5. 6. 30 o 65 o 80 o 40 o 15 o 30 o 165 o 35 o 140 o 60 o 115 o 60 o 45 o 165 o 15 o 145 o 40 o

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Using Algebra xoxo 3x o Find angle x The angles on a straight line add upto 180 0 So x + 3x = 180 4x = 180 x × 4 = 180Reverse the order 180 ÷ 4 = xx = 45 o

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Using Algebra xoxo 2x o Find angle x The angles around a point add upto 360 0 So x + 2x + 120 + 90 = 360 3x + 210 = 360 x × 3 + 210 = 360Reverse the order 360 - 210 ÷ 3 = x 150 ÷ 3 = xx = 50 o 90 o 120 o

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Small textbook P 54 Questions 1, 2 & 3

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The Angles of a Triangle A B C A B C If the corners are torn off and placed together as shown then the angles make a straight line – 180 o So the angles of a triangle add upto 180 o

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The Angles of a Triangle 50 o 100 o 30 o The missing angle is 30 o ( angles of a triangle add upto 180 0 ) The missing angles are and 150 o 110 o 30 o 40 o 30 o 40 o ( angles on a straight line add upto 180 0 ) ( angles of a triangle add upto 180 0 )

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Find the missing angles 1. 2. 3. 4. 5. 30 o 65 o 80 o 140 o 50 o 60 o 125 o 45 o 60 o 15 o 60 o 70 o 55 o 80 o 100 o 40 o 120 o 125 o

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2 Special Triangles Isosceles Triangle 2 Equal Sides 2 Equal Angles

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2 Special Triangles Equilateral Triangle 3 Equal Sides 3 Equal Angles – all 60 o

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130 o Find the missing angles 50 o 80 o Angles on a straight line add upto 180 Base angles of an isosceles triangle are equal Angles of a triangle add upto 180

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18 o Find the missing angles 81 o 99 o Angles on a straight line add up to 180 Angles of a triangle add upto 180 and the base angles of an isosceles triangle are equal : 180 – 18 = 162 So each base angle = 81as 162 ÷ 2 = 81

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