1. © T Madas

3. What do the 3 angles of any triangle add up to? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

4. © T Madas What do the 3 angles of any triangle add up to? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

5. © T Madas

6. The angles in a triangle add up to 180°

7. The angles in a triangle add up to 180°

8. The angles in a triangle add up to 180°

9. © T Madas

10. Angle Calculations in Triangles – 125° =55°180° + 50° =125°75° – 119° =61°180° + 90° =119°29° 75° 55° 50° 29° 61°

11. © T Madas Angle Calculations in Triangles ÷ 2 =70°140° – 40° =140°180° – 70° =110°180° + 35° =70°35° 40° 70° 35° 110°

12. © T Madas Practice Angle Calculations with Triangles

13. 70° 60° 50° 55° 45° 80° 45° 35° 100° 25° 65° 70° 45° 30° 35° 115° 75° 55° 50° 35° 25° 120°

14. © T Madas 65° 70° 45° 52° 48° 80° 43° 33° 104° 29° 61° 62° 71° 47° 33° 38° 109° 77° 52° 51° 39° 24° 117°

15. © T Madas 60° 80° 40° 53° 47° 80° 43° 36° 101° 26° 64° 61° 71° 48° 32° 38° 110° 78° 52° 50° 40° 23° 117°

16. © T Madas 40° 70° 55° 65° 50° 45° 35° 110° 80° 20° 70° 100° 40°

17. © T Madas Quick Test on Angle Calculations with Triangles

18. 70° 60° 50° 55° 45° 80° 45° 35° 100° 25° 65° 70° 45° 30° 35° 115° 75° 55° 50° 35° 25° 120°

19. © T Madas 65° 70° 45° 52° 48° 80° 43° 33° 104° 29° 61° 62° 71° 47° 33° 38° 109° 77° 52° 51° 39° 24° 117°

20. © T Madas 60° 80° 40° 53° 47° 80° 43° 36° 101° 26° 64° 61° 71° 48° 32° 38° 110° 78° 52° 50° 40° 23° 117°

21. © T Madas 40° 70° 55° 65° 50° 45° 35° 110° 80° 20° 70° 100° 40°

22. © T Madas

23. 180° What do the 4 angles in a quadrilateral add up to? 360°

24. © T Madas Practice Angle Calculations with Quadrilaterals

25. 90° 95° 65° 110° 150° 50° 100° 60° 160° 40° 110° 50° 30° 95° 75° 160° 75° 105° 115° 65° 75° 45° 80° 160° 155° 60° 115° 30° 155° 70° 100° 35° 95° 65° 105° The angles of a quadrilateral add up to 360°

26. © T Madas 90° 95° 70° 105° 150° 45° 100° 65° 160° 45° 110° 45° 35° 95° 70° 160° 65° 115° 120° 60° 75° 45° 75° 165° 150° 65° 115° 30° 150° 75° 100° 35° 100° 95° 55° 110° The angles of a quadrilateral add up to 360°

27. © T Madas 91° 92° 73° 105° 152° 46° 97° 65° 159° 44° 111° 46° 33° 94° 69° 164° 64° 114° 119° 63° 74° 44° 74° 168° 149° 68° 115° 28° 155° 72° 97° 36° 91° 92° 79° 98° The angles of a quadrilateral add up to 360°

28. © T Madas Quick Test on Angle Calculations with Quadrilaterals

29. The angles of a quadrilateral add up to 360° 90° 95° 65° 110° 150° 50° 100° 60° 160° 40° 110° 50° 30° 95° 75° 160° 75° 105° 115° 65° 75° 45° 80° 160° 155° 60° 115° 30° 155° 70° 100° 35° 95° 65° 105° test

30. © T Madas The angles of a quadrilateral add up to 360° 90° 95° 70° 105° 150° 45° 100° 65° 160° 45° 110° 45° 35° 95° 70° 160° 65° 115° 120° 60° 75° 45° 75° 165° 150° 65° 115° 30° 150° 75° 100° 35° 100° 95° 55° 110° test

31. © T Madas 91° 92° 73° 105° 152° 46° 97° 65° 159° 44° 111° 46° 33° 94° 69° 164° 64° 114° 119° 63° 74° 44° 74° 168° 149° 68° 115° 28° 155° 72° 97° 36° 91° 92° 79° 98° test The angles of a quadrilateral add up to 360°

32. © T Madas

33. x 21° 29° 69° 61° 50° Calculate the angle marked as x.

34. © T Madas

35. Calculate the angle marked as x x 50° 70° 130° 20° 30°

36. © T Madas

37. 49° x 41° Calculate the angle marked as x. 49°

38. © T Madas

39. 140° 40° 70° Calculate the three angles of the triangle 110° 70° 55° Calculate the angle marked with x x

40. © T Madas

41. 136° 44° 68° Calculate the angle marked with x x 292°

42. © T Madas

43. 50° 70° 55° 65° Calculate the missing angles in each triangle

44. © T Madas

45. One of the angles of a rhombus is 47°. Calculate the angle marked as x. 47° x Opposite angles in a parallelogram are equal A rhombus is a special parallelogram Angles in any quadrilateral add up to 360° 47 + 47 94 360 – 94 266 ÷2=133°

46. © T Madas

47. One of the angles of an isosceles triangle is 64°. What are the sizes of the other two angles? [You must show that there are 2 different possibilities] 64° 52° 64° 58° 1 st possibility2 nd possibility 64 + 64 128 180 – 128 52 116÷2=58° 180 – 64 116

48. © T Madas

49. A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below. B 20° 50° 55° 1.Calculate the four angles of the parallelogram. 2.Using the properties of parallelograms (including special parallelograms), explain why this drawing is impossible. C R CAD = R BCA : alternating angles 20° D A

50. © T Madas A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below. D B 20° 50° 55° 1.Calculate the four angles of the parallelogram. 2.Using the properties of parallelograms (including special parallelograms), explain why this drawing is impossible. 20° R ACD = R BAC : alternating angles 50° we could use: opposite angles in any parallelogram are equal or R CAD = R BCA : alternating angles A C

51. © T Madas A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below. D B 20° 50° 55° 1.Calculate the four angles of the parallelogram. 2.Using the properties of parallelograms (including special parallelograms), explain why this drawing is impossible. 20° 50° A C 70 + 70 140 360 – 140 220 ÷2=110° we could use: opposite angles in any parallelogram are equal or 110°

52. © T Madas In any parallelogram both diagonals bisect their angles: both diagonals do not bisect their angles: only one diagonal bisect its angles: Can you think of a quadrilateral where only one diagonal bisect its angles? A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below. D B 20° 50° 55° 1.Calculate the four angles of the parallelogram. 2.Using the properties of parallelograms (including special parallelograms), explain why this drawing is impossible. 20° 50° A C 110° 55°, square, ordinary parallelogram rhombus rectangle NONE there is no parallelogram with only one diagonal bisecting its angles

53. © T Madas