This document discusses different types of angles and angle theorems. It defines right, acute, obtuse, and reflex angles. It explains that the internal angles of a regular polygon sum to 180(n-2) degrees and the external angles sum to 360 degrees. It presents several angle theorems including: angles at a point sum to 360 degrees; angles on a straight line sum to 180 degrees; opposite angles are equal; corresponding angles are equal; alternate angles are equal; and supplementary angles sum to 180 degrees. Examples are provided to demonstrate applying these theorems.

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

2. Key wordsacuteobtuserotationreflexinternalexternaltheoremoppositeparallelcorrespondingalternatesupplementary

3. Angle B or angle ABC or angle CBAACWhich is the largest angle?BGBDFEIEHH

4. Types of anglesRight angleacute90°obtuse180°reflex

5. External angleInternal angle

6. 360°540°720°1080°

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

8. 360°÷ 4540°÷ 590°108°720°÷ 61080°÷ 8135°120°

9. 90°72°60°45°

10. Now try these1. 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 theoremsA 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 linesF angles: Corresponding angles (a and b) are equal

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

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

19. Now try these