1. Angles BTESSSBAT: measure angles, identify angles, find the internal and external angles of regular polygons and use angle theorems to solve problems

2. Key words acute obtuse rotation reflex internal external theorem opposite parallel corresponding alternate supplementary

3. Angle B or angle ABC or angle CBA A C Which is the largest angle? B G B D F E I E H H

4. Types of angles Right angle acute 90° obtuse 180° reflex

5. External angle Internal angle

6. 360° 540° 720° 1080°

7. 360° 540° 180° in a triangle: 720° 1080°

8. 360° ÷ 4 540° ÷ 5 90° 108° 720° ÷ 6 1080° ÷ 8 135° 120°

9. 90° 72° 60° 45°

10. Now try these 1. A regular dodecagon has 12 sides. Find its internal angle. 2. A regular polygon has an external angle of 36° - how many sides does it have? What is its internal angle?

11. Angle theorems A theorem is a law that is always true. 360° Angles at a point add up to 87° 55° 133° 85°

12. Angles on a straight line add up to 180° 85° 35° 60°

13. X- angles: opposite angles are equal 110° 70° 70° 110°

14. X- angles: opposite angles are equal 100° In fact we only need to know one angle: 80° 80° 100°

15. Now try these

16. Angles using parallel lines F angles: Corresponding angles (a and b) are equal

17. Angles using parallel lines Z angles: alternate angles (c and d) are equal

18. Angles using parallel lines Supplementary angles (a and c) add up to 180°

19. Now try these