Math topic中文

Recognising angles and their sizes

Recognising angles in real-life contexts, understanding comparison of their sizes, and converting between degrees-minutes-seconds and decimal degrees.

Practice questions

  1. 1In the figure, WXYZ is a trapezium and AXYB is a rhombus. XBC and XAZ are straight lines. WX // ZY, BC = BY, ∠XAB=82∘\angle XAB = 82^\circ…
  2. 2In the figure below, ABCD is a trapezium. AF and EC are straight lines. Peishan wrote four statements to describe the fi…
  3. 3In the figure below, ABGF and BCDG are rhombuses. ∠ABF=31∘\angle ABF = 31^\circ, ∠CBG=40∘\angle CBG = 40^\circ and EF is parallel to…
  4. 4In the figure, PQ = PS and SRP is a straight line. Find ∠RQS\angle\text{RQS}. Ans: ___ ∘^\circ
  5. 53.76°= 度 分 秒．
  6. 6In the figure below, WPRT is a square. QWU and SWV are straight lines. ∠QWP=13∘\angle QWP = 13^\circ and ∠TWS=28∘\angle TWS = 28^\circ…
  7. 7In the figure below, ABCD is a square and CEFG is a rectangle. ∠GCD=203∘\angle\text{GCD} = 203^\circ. Find ∠BCE\angle\text{BCE}.…
  8. 8The figure below is not drawn to scale. PQRT is a parallelogram. ∠TPQ=115∘\angle\text{TPQ} = 115^\circ and ∠SQP=43∘\angle\text{SQP} = 43^\circ…
  9. 9ABC is a triangle, BFC is a straight line and ∠DEF\angle DEF is a right angle. Find ∠BEF\angle BEF. Circle the words that de…
  10. 10计算：153°-26°40′= ．
  11. 11In the figure below, PQ and QR are drawn to scale. Draw 2 lines, PS and SR so that PQRS is a parallelogram. Measure ∠QPT\angle QPT…
  12. 12In the figure below, A and B are two points on a map. Point A is north of B. Point C is east of B and ∠BAC=50∘\angle\text{BAC} = 50^\circ…
  13. 13The figure below is not drawn to scale. ABE is an equilateral triangle and BCD is an isosceles triangle. ABC and BDF are…
  14. 14In the figure, ABCD is a trapezium and BCEF is a square. ∠DCE=203∘\angle DCE = 203^\circ. Find ∠ABC\angle ABC. Ans: ___ ∘^\circ
  15. 15In the figure below, EFG is an isosceles triangle. DEG is a straight line and EG=FGEG = FG. ∠DEF=111∘\angle DEF = 111^\circ and ∠HGE=63∘\angle HGE = 63^\circ…
  16. 16PQRS is a rectangle and STUV is a square. Find ∠PSU\angle\text{PSU}.
  17. 17在时刻8：30时，时钟上的时针与分针之间的所成的夹角是（ ） A. 60° B. 70° C. 75° D. 85°
  18. 18In the figure below, AB and CD are straight lines. Find ∠p\angle p.
  19. 19In the figure, QR and ST are straight lines. Find ∠m\angle m.
  20. 20下面的语句中，正确的是( ) A. 线段AB和线段BA是不同的线段 B. ∠AOB和∠BOA是不同的角 C. “延长线段AB到C”与“延长线段BA到C”意义不同 D. “连接AB”与“连接BA”意义不同
  21. 21PQRS is a parallelogram. Find ∠z\angle z.
  22. 22Refer to the square grid below and answer question 9. Which of the following statements is TRUE of the diagram shown abo…
  23. 23角的大小是由（ ）决定的。 A. 边的长短 B. 两条边叉开的大小
  24. 24在时钟的钟面上，5：30时，时针与分针的夹角为 ．
  25. 25ABCD is a trapezium. ∠p=∠q\angle p = \angle q. Find the sum of ∠r\angle r and ∠s\angle s. Ans : _____________\…
  26. 26STUV is a trapezium. UVWX is a rhombus. Find ∠y\angle y. Ans: ___
  27. 27时钟里，时针从55时整的位置起，___min⁡\min后与分针第一次重合．
  28. 28The square grid below shows the positions of points A, B, C, D, E, F and G. In what direction is point E from point B? A…
  29. 29若∠A ＝ 20°18′，∠B ＝ 20°15′30″，∠C ＝ 20.25°，则（ ） A. ∠A＞∠B＞∠C B. ∠B＞∠A＞∠C C. ∠A＞∠C＞∠B D. ∠C＞∠A＞∠B
  30. 30AEF and CEF are isosceles triangles with AE = EF = CE. Find ∠AFB\angle\text{AFB}.
  31. 31The map below shows the locations of four cities that are linked by railroads. Which one of the following statements is…
  32. 32In the figure below, ABCD is a square and CEFG is a rectangle. ∠GCD=203∘\angle GCD = 203^\circ. Find ∠BCE\angle BCE. Answer: ___
  33. 33∠α=48°26′，则∠α的余角等于 ，∠α的补角等于 ．
  34. 34一天24小时中，时钟的分针和时针共组合成 次平角， 次周角．
  35. 35The figure below is not drawn to scale. ABEF is a parallelogram and BCDE is a trapezium. BE//CD, AB//FD and BC//AD. DF i…
  36. 36若∠α的余角是45°32′，则∠α的补角为 ___ ．
  37. 37The figure below is formed by a square ABCD, equilateral triangle ABE and triangles BDG and BEG. AFE and BFD are straigh…
  38. 38把一个平角分成两个角，其中一个是锐角，另一个角一定是（ ） A. 钝角 B. 平角 C. 锐角 D. 直角
  39. 39In the figure below, ABCD is a rhombus. AE, FC and BFD are straight lines. Find ∠DAE\angle DAE.
  40. 4092.76°= 度 分 秒；22°32′24″= 度．
  41. 41把平角分成180等份，每一分所对的角就是 度的角．30份所对的角是 度角，是 角．
  42. 42Kamie is standing at K facing north. Kamie turns through an angle of 135exto135^ ext{o} in an anti-clockwise direction, follo…
  43. 43Gayatri is standing at point Q facing the market. Which place will she be facing if she turns 225∘225^\circ anti-clockwise…
  44. 44如果一个角是10°10°，用66倍的放大镜观察，这个角应是___°.°.
  45. 45钟表上一个大格是___度，一个小格是___度．5时的时候时针和分针的夹角是___，9时的时候时针和分针的夹角是___度．当钟表是___时的时候，时针分针的夹角是180度．
  46. 46下列关系式正确的是（ ） A. 35.5°=35°5′ B. 35.5°=35°50′ C. 35.5°＜35°5′ D. 35.5°＞35°5′
  47. 47在时刻8∶30时，时钟上的时针与分针间的夹角是 A. 75° B. 85° C. 70° D. 60°
  48. 48At first, Julian and Kelvin were facing the same direction. Julian then turned 45∘45^\circ anti-clockwise while Kelvin tu…
  49. 49In the diagram, point A is north of point B and ∠ABC=135∘\angle\text{ABC} = 135^\circ. In what direction is point C from point…
  50. 50In the figure below, EFGH is a rhombus and FGJK is a trapezium. EH and KF are straight lines. ∠KLH=55∘\angle KLH = 55^\circ an…
  51. 51直角的3倍是___度，周角里有___个平角．
  52. 52Study the square grid below. Which line in the square grid is perpendicular to BC?
  53. 53In the figure below, WPRT is a square. QWU and SWV are straight lines. ∠QWP=13∘\angle QWP = 13^\circ and ∠SWT=28∘\angle SWT = 28^\circ…
  54. 54In the figure, how many of the six marked angles are greater than 90∘90^\circ?
  55. 55计算 (1)90∘−78∘19′40″(1)90^{\circ}-78^{\circ}19′40″； (2)11∘23′26″×3(2)11^{\circ}23′26″×3．
  56. 56The square grid shows the positions of A, B, C, D, E, F, G and H. In the square grid, point ___ is north-west of point G…
  57. 57Sam had a trapezium ABCD and an equilateral triangle EFG. He folded the trapezium along the line DH to form a parallelog…
  58. 58720分= 时 120秒= 分 1平角= 直角．
  59. 59In the figure below, ABCD is a trapezium. APB, DQC, RCS and PQR are straight lines. APB is parallel to DQC and AD is par…
  60. 60ABCD is a rectangle. AE and DG are straight lines. ∠ADF=∠FDE\angle ADF = \angle FDE. Find ∠FDE\angle FDE. Find ∠BGD\angle BGD. Find…