1. Angles, Angles of Triangles and Parallel Lines

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

3. 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.

4. 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

5.  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

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

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

8. 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

9. 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

10. 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

11. 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

12. Small textbook P 54 Questions 1, 2 & 3

13. 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

14. 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 )

15. 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

16. 2 Special Triangles Isosceles Triangle 2 Equal Sides 2 Equal Angles

17. 2 Special Triangles Equilateral Triangle 3 Equal Sides 3 Equal Angles – all 60 o

18. 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

19. 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