Math topic中文

Angle relationships

vertically opposite angles, angles on a straight line and angles at a point

Practice questions

  1. 1In triangle ABC, ∠ABC=90∘\angle ABC = 90^\circ, BX=2XCBX = 2XC and sin⁡∠AXC=35\sin \angle AXC = \dfrac{3}{5}. Express as a fraction in its…
  2. 2A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  3. 3The diagram shows the positions of a harbour, H, a lighthouse, L, and two buoys P and Q. HPQ is a straight line. The bea…
  4. 4∠A=52°∠A=52°，则∠A∠A的余角是()(\quad) A. 148°148° B. 138°138° C. 48°48° D. 38°38°
  5. 5The figure is made up of a regular pentagon ABCDE and a regular hexagon CDFGHI. Find angle BCI. Answer ... ° Determine w…
  6. 6Vinesh has a rectangular piece of paper. He folded it along the dotted lines without overlapping as shown below. Find ∠x\angle x…
  7. 7A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  8. 8The diagram shows a regular hexagon P and a regular n-sided polygon Q. Polygon Q has an exterior angle of 18°. Find the…
  9. 9如果∠A∠A的补角与∠A∠A的余角互补，那么2∠A2∠A是()() A. 锐角 B. 直角 C. 钝角 D. 以上三种都可能
  10. 10In the diagram, PQRS is a vertical rectangular wall of height 2.5 m and length 7.5 m. T is a point on level ground from…
  11. 11The diagram shows a circle PQRST, with centre O. PV and RV are tangents to the circle and U is the intersection of PS an…
  12. 12In the diagram ABCDE is a regular pentagon. BE and BD are straight lines. Find, giving reasons for each answer, angle AB…
  13. 13A, B and C are points on the circle with centre O. Q and R are points on the circle with centre P. CSR and BSQ are tange…
  14. 14正多边形的一个内角是150∘150{^{\circ}}，则这个正多边形的边数为()({ }) A. 1010 B. 1111 C. 1212 D. 1313
  15. 15In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  16. 16The diagram shows two circles that touch at C. A, B and C are points on the small circle, centre P. C, D and E are point…
  17. 17已知∠A=55°，则它的余角的大小是___．
  18. 18In the figure below, a rectangular piece of paper was folded as shown. Given that ∠GHF\angle \text{GHF} is 48∘48^\circ, fin…
  19. 19下列四个命题：①①带根号的数是无理数；②②如果∠A=∠B∠A=∠B，那么∠A∠A与∠B∠B是对顶角；③③经过直线外一点有且只有一条直线与已知直线平行；④④在平面直角坐标系中，如果点P(m,n)P(m,n)到xx…
  20. 20The diagram shows a parallelogram ABCD on horizontal ground where AC is a path. AB = 15 m and BC = 8 m. The bearing of B…
  21. 21The diagram shows a semi-circle BAC, with diameter BC = 34 cm. AD and BCD are straight lines. Given that cos⁡∠ABC=817\cos\angle ABC = \dfrac{8}{17}…
  22. 22In the diagram, P, Q, R and S are points on a circle. PR and QS meet at T. Show that triangle PTS and triangle QTR are s…
  23. 23若一个正多边形的一个内角是120°，则这个正多边形的边数是（ ） A. 9 B. 8 C. 6 D. 4
  24. 24The diagram above shows a park ABCDABCD that is on horizontal ground, crossed by a straight path ACAC. Point BB is due no…
  25. 25如果一个角的余角比这个角大30°，则这个角的补角的度数是 ．
  26. 26The points A, B, E and D lie on the circle with centre O. BEC is a straight line and BF is a tangent to the circle at po…
  27. 27The diagram below shows part of a regular 18-sided polygon, ABCDEF... The lines BC and ED are extended to meet at the po…
  28. 28ABCD is a square and AQ is perpendicular to PR. PQR and ADR are straight lines. DQ : DC = 1 : 2. Show that triangle DQR…
  29. 29Airport B is 500 km away from airport A on a bearing of 064°. An aircraft leaves airport A at 22 45 on Monday to fly to…
  30. 30The diagram above shows a kite ABCD where angle BAC = 30°. EB, BD and DF are three sides of a regular polygon. ABE and A…
  31. 31下列语句中，不是真命题的是（ ） A. 两个锐角的和是钝角 B. 直角的补角是直角 C. 对顶角相等 D. 两直线平行，同位角相等
  32. 32一个角的度数是40°，则这个角的补角是___．
  33. 33The scale of a map is 5 cm : 1 km. A reservoir has an actual area of 0.7 km^2. Find the area, in square centimetres, of…
  34. 34In the diagram, ABCD is a rectangle. OAB is a sector of a circle, centre O. OXD and OYC are straight lines. Show that tr…
  35. 35下列命题中，是真命题的是()(\quad) A. 内错角相等 B. 对顶角相等 C. 若x2=4x^{2}=4，则x=2x=2 D. 若a>ba>b，则a2>b2a^{2}>b^{2}
  36. 36The diagram shows a pentagon. Three of the interior angles are 100° each. One of its exterior angle is 50°. Find the val…
  37. 37若∠1的补角为130°，则∠1的余角的度数为 ．
  38. 38The diagram shows the positions of four checkpoints W, X, Y and Z in a jungle reserve area. The checkpoints are connecte…
  39. 39In the diagram, BDCE is a straight line. BD = 4 cm, AC = 10 cm and AB = AD. Given that the area of triangle ABD is 16 cm…
  40. 40如图，△ABC中，∠C=70°，∠B=30°，将△ABC绕点A顺时针旋转后，得到△AB´C´，且C´在边BC上，则∠B´C´B的度数为（ ） A. 30° B. 40° C. 46° D. 60°
  41. 41Regular pentagons and squares of the same sides are placed together in a pattern as shown in the diagram. Caleb claims t…
  42. 42下列命题是假命题的是()(\quad) A. 对顶角相等 B. 两直线平行，同位角相等 C. 内错角相等，两直线平行 D. 三角形的外角大于内角
  43. 43PQRS are points on the circumference of a circle, centre O. Angle OQR = 50°, angle PSR = 73° and obtuse angle SOQ = 156°…
  44. 44In the diagram, ABC is an equilateral triangle, ACDE is a square and angle FAC = 15°. Show that triangle EAF and triangl…
  45. 45A regular polygon has interior angles of 140°. Find the number of sides of the polygon The diagram shows a sketch of a r…
  46. 46The equation of the line l1l_1 is x+4y=20x + 4y = 20. The line cuts the x-axis at point A and the y-axis at point B. Another…
  47. 47若铺地面的瓷砖每一个顶点处都有六个相同的正多边形组成，则这种正多边形只能是（ ） A. 正三角形 B. 正方形 C. 正五边形 D. 正六边形
  48. 48一个正多边形的每一个内角都等于140°，则它的每一个外角都等于 度，它是 边形．
  49. 49In the diagram, A, B, C and D are four points on a circle, centre O. Angle ABO=x∘ABO = x^\circ and angle ADO=y∘ADO = y^\circ. Fi…
  50. 50如果∠α=60°，那么∠α的余角的度数是（ ） A. 30° B. 60° C. 90° D. 120°
  51. 51B, C, D, E and F are points on the circle with centre O. AE is tangent to the circle and ABC is a straight line. ∠BAE=38∘\angle BAE = 38^\circ…
  52. 52O is the centre of the circle passing through B, E, D and C. Angle DOC=84∘DOC = 84^\circ and angle CBO=54∘CBO = 54^\circ. PQPQ is…
  53. 53P, Q, R and S are four villages located on an island, where Q is due north of R. PQ = 924 m, QR = 640 m, PR = 1124 m, RS…
  54. 54In the diagram, ABC and ACD are triangles such that angle ACB = angle ADC. Show that the two triangles are similar. Answ…
  55. 55The diagram shows four points P, Q, R and S on level ground. Q is due east of P. Angle SPQ = 40° and angle PSR = 15°. PQ…
  56. 56∠α=48°26′，则∠α的余角等于 ，∠α的补角等于 ．
  57. 57若∠α的余角是45°32′，则∠α的补角为 ___ ．
  58. 58A, B, C, D and E are points on the circle, centre O. QP and QR are tangents to the circle at B and E respectively. AC in…
  59. 59In the diagram, OAB is a sector of a circle with centre O. Given that OA = 12 cm, ∠AOB = θ\theta radians, OC = 8 cm and…
  60. 60下列正确说法的个数是( ) ①① 同位角相等 ②② 对顶角相等 ③③ 等角的补角相等 ④④ 两直线平行，同旁内角相等 A. 11 B. 22 C. 33 D. 44