Mathematics Shape and Space: Polygon Angles

1. a place of mind FACULTY OF EDUCATION Department of Curriculum and Pedagogy MathematicsShape and Space: Polygon Angles Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund 2012-2013

2. Polygon Angles

3. Polygon Angles I What is the sum of all internal angles in this equilateral triangle? • 90° • 180° • 270° • 360° • No idea

4. Solution Answer: B Justification: The sum of all internal angles in an equilateral triangle is 180°.

5. Polygon Angles II What is the internal angle of this equilateral triangle? • 30° • 60° • 90° • 180° • No idea

6. Solution Answer: B Justification: The sum of all internal angles is 180°, and the triangle has three corners, so 180/3=60°.

7. Polygon Angles III What is the external angle of this equilateral triangle? • 30° • 60° • 90° • 120° • 180°

8. Solution Answer: D Justification: The internal angle and external angle add up to 180° because they share a straight line.

9. Polygon Angles IV What is the sum of all external angles in this equilateral triangle? • 90° • 180° • 270° • 360° • No idea

10. Solution Answer: B Justification: The sum of all external angles in an equilateral triangle is 3×120=360°.

11. Polygon Angles V What is the internal angle of this square? • 30° • 60° • 90° • 180° • No idea

12. Solution Answer: C Justification: Squares have perpendicular sides and bases, which have a right angle of 90°.

13. Polygon Angles VI What is the sum of all internal angles in this square? • 90° • 180° • 270° • 360° • No idea

14. Solution Answer: D Justification: The sum of all internal angles in an square is 4×90=360°.

15. Polygon Angles VII What is the external angle of this square? • 30° • 60° • 90° • 120° • 180°

16. Solution Answer: C Justification: The internal angle and external angle add up to 180° because they share a straight line.

17. Polygon Angles VIII What is the sum of all external angles in this square? • 90° • 180° • 270° • 360° • No idea

18. Solution Answer: D Justification: The sum of all external angles in a square is 4×90=360°.

19. Polygon Angles IX What is the sum of all internal angles in this regular pentagon? • 180° • 360° • 540° • 720° • No idea

20. Solution Answer: C Justification: The sum of all internal angles in a pentagon is the same as three triangles (see picture below).

21. Polygon Angles X What is the internal angle of this regular pentagon? • 54° • 72° • 108° • 144° • No idea

22. Solution Answer: C Justification: A pentagon has 5 corners, thus each internal angle is 540/5=108°.

23. Polygon Angles XI What is the external angle of this regular pentagon? • 54° • 72° • 108° • 144° • No idea

24. Solution Answer: B Justification: The internal angle and external angle add up to 180° because they share a straight line.

25. Polygon Angles XII What is the sum of all external angles in this regular pentagon? • 90° • 180° • 270° • 360° • No idea

26. Solution Answer: D Justification: The sum of all external angles in a regular pentagon is 5×72=360°.

27. Polygon Angles XIII What is the sum of all internal angles in this regular hexagon? • 180° • 360° • 540° • 720° • No idea

28. Solution Answer: D Justification: The sum of all internal angles in a hexagon is the same as four triangles (see picture below).

29. Polygon Angles XIV What is the internal angle of this regular hexagon? • 60° • 90° • 120° • 144° • No idea

30. Solution Answer: C Justification: A hexagon has 6 corners, thus each internal angle is 720/6=120°.

31. Polygon Angles XV What is the external angle of this regular hexagon? • 60° • 90° • 120° • 144° • No idea

32. Solution Answer: A Justification: The internal angle and external angle add up to 180° because they share a straight line.

33. Polygon Angles XVI What is the sum of all external angles in this regular hexagon? • 90° • 180° • 270° • 360° • No idea

34. Solution Answer: D Justification: The sum of all external angles in a regular hexagon is 6×60=360°.

35. Polygon Angles XVII What is the sum of all internal angles in this regular heptagon? • 540° • 720° • 900° • 1080° • No idea

36. Solution Answer: C Justification: The sum of all internal angles in a heptagon is the same as five triangles (see picture below).

37. Polygon Angles XVIII What is the internal angle of this regular heptagon? • 70° • ~129° • ~142° • ~157° • No idea

38. Solution Answer: B Justification: A heptagon has 7 corners, thus each internal angle is 900/7≈129°.

39. Polygon Angles XIX What is the external angle of this regular heptagon? • ~37° • ~42° • ~51° • ~62° • No idea

40. Solution Answer: C Justification: The internal angle and external angle add up to 180° because they share a straight line.

41. Polygon Angles XX What is the sum of all external angles in this regular heptagon? • 90° • 180° • 270° • 360° • No idea

42. Solution Answer: D Justification: The sum of all external angles in a regular heptagon is 7×51.2857…=360°.

43. Polygon Angles XXI What is the sum of all internal angles in this regular octagon? • 540° • 720° • 900° • 1080° • No idea

44. Solution Answer: D Justification: The sum of all internal angles in a octagon is the same as six triangles (see picture below).

45. Polygon Angles XXII What is the internal angle of this regular octagon? • 90° • 110° • 120° • 135° • No idea

46. Solution Answer: D Justification: An octagon has 8 corners, thus each internal angle is 1080/8=135°.

47. Polygon Angles XXIII What is the external angle of this regular octagon? • 20° • 30° • 45° • 60° • No idea

48. Solution Answer: C Justification: The internal angle and external angle add up to 180° because they share a straight line..

49. Polygon Angles XXIV What is the sum of all external angles in this regular octagon? • 90° • 180° • 270° • 360° • No idea

50. Solution Answer: D Justification: The sum of all external angles in a regular octagon is 8×45=360°.