Geometric Problem Solving (Lines, Angles, Polygons) · CSEC Mathematics

96 past-paper questions on Geometric Problem Solving (Lines, Angles, Polygons), part of GEOMETRY AND TRIGONOMETRY, from every CSEC Mathematics paper on Quelpr.

1. 4(d)(i)1 mark· CSEC Mathematics · 2003 (Specimen) · Paper 2Calculate the size of angle g in the given figure.
2. 4(d)(ii)1 mark· CSEC Mathematics · 2003 (Specimen) · Paper 2Calculate the size of angle e in the given isosceles triangle figure.
3. 6(c)2 marks· CSEC Mathematics · 2009 (second paper) · Paper 2State ONE reason why KL is parallel to NM.
4. 6(d)1 mark· CSEC Mathematics · 2009 (second paper) · Paper 2What type of quadrilateral is KLMN?
5. 3(a)(i)1 mark· CSEC Mathematics · 2021 · Paper 2Calculate the size of angle PRQ.
6. Q531 mark · multiple choice· CSEC Mathematics · January 2011 · Paper 1In the diagram, AB is parallel to CD, and \angle JKB = 125^\circ. \angle MLD is
7. Q561 mark · multiple choice· CSEC Mathematics · January 2011 · Paper 1AB is parallel to EC. Calculate \angle BDE.
8. Q591 mark · multiple choice· CSEC Mathematics · January 2011 · Paper 1How many triangles congruent to \Delta ADE would be needed to cover the rectangle ABCD entirely?
9. Q531 mark · multiple choice· CSEC Mathematics · January 2013 · Paper 1In the diagram AB and CD are parallel. Which of the following BEST describes the relation between x and y?
10. Q561 mark · multiple choice· CSEC Mathematics · January 2013 · Paper 1The length of MO, in centimetres, is
11. Q521 mark · multiple choice· CSEC Mathematics · January 2014 · Paper 1Which of the following angles are equal?
12. Q531 mark · multiple choice· CSEC Mathematics · January 2014 · Paper 1The measure of angle ABE is
13. Q581 mark · multiple choice· CSEC Mathematics · January 2014 · Paper 1The length of MO, in centimetres, is
14. Q541 mark · multiple choice· CSEC Mathematics · January 2017 · Paper 1AC and DE are straight lines intersecting at B. Angle DBA = 58^\circ. The measure of angle ABE is
15. Q571 mark · multiple choice· CSEC Mathematics · January 2017 · Paper 1In triangle ABC, angle A = x^\circ and angle B = 2x^\circ. What is the size of angle C?
16. Q531 mark · multiple choice· CSEC Mathematics · May/June 2011 · Paper 1In the diagram, AB and CD are parallel. Which of the following BEST describes the relation between x and y?
17. Q541 mark · multiple choice· CSEC Mathematics · May/June 2011 · Paper 1The measure of angle ABE is
18. Q571 mark · multiple choice· CSEC Mathematics · May/June 2011 · Paper 1AB is parallel to EC. What is the measure of \angle BDE?
19. Q531 mark · multiple choice· CSEC Mathematics · May/June 2012 · Paper 1If the sum of the interior angles of a polygon is 4 right angles, the polygon is a
20. Q561 mark · multiple choice· CSEC Mathematics · May/June 2012 · Paper 1In the triangle, the value of x is
21. Q591 mark · multiple choice· CSEC Mathematics · May/June 2012 · Paper 1In a triangle ABC, angle A = x^\circ and angle B = 2x^\circ. What is the size of angle C?
22. Q521 mark · multiple choice· CSEC Mathematics · May/June 2013 · Paper 1If the sum of the interior angles of a polygon is 4 right angles, then the polygon is a
23. Q531 mark · multiple choice· CSEC Mathematics · May/June 2013 · Paper 1In the diagram AB and CD are parallel. Which of the following BEST describes the relation between x and y?
24. Q561 mark · multiple choice· CSEC Mathematics · May/June 2013 · Paper 1How many triangles congruent to \Delta ADE would be needed to cover the rectangle ABCD entirely?
25. Q521 mark · multiple choice· CSEC Mathematics · May/June 2015 · Paper 1If the sum of the interior angles of a polygon is 4 right angles, then the polygon is a
26. Q531 mark · multiple choice· CSEC Mathematics · May/June 2015 · Paper 1Item 53 refers to the following diagram. In the diagram, AB and CD are parallel. Which of the following BEST describes the relation between x and y?
27. Q541 mark · multiple choice· CSEC Mathematics · May/June 2015 · Paper 1Item 54 refers to the triangle below. In the triangle, the value of x is
28. Q561 mark · multiple choice· CSEC Mathematics · May/June 2015 · Paper 1Item 56 refers to the following pair of similar triangles. The length of MO, in centimetres, is
29. Q541 mark · multiple choice· CSEC Mathematics · May/June 2016 · Paper 1Item 54 refers to the following diagram. In the diagram AB and CD are parallel. Which of the following BEST describes the relation between x and y?
30. Q561 mark · multiple choice· CSEC Mathematics · May/June 2016 · Paper 1Item 56 refers to the following diagram. In the diagram, AB is parallel to EC. The measure of \angle BDE is
31. Q581 mark · multiple choice· CSEC Mathematics · May/June 2016 · Paper 1Item 58 refers to the following diagram. In the isosceles triangle shown above, the value of x is
32. 3(a)3 marks· Mathematics Q3 3(a)Complete the following statement: The prism has ____ faces, ____ edges and ____ vertices.
33. 3(a)(i)2 marks· Mathematics Q3 3(a)(i)Giving the reason for each step of your answer, calculate the size of ∠ LNK
34. 3(a)(ii)2 marks· Mathematics Q3 3(a)(ii)Giving the reason for each step of your answer, calculate the size of ∠ NLM
35. 3(a)(iii)2 marks· Mathematics Q3 3(a)(iii)Giving the reason for each step of your answer, calculate the size of ∠ KNM.
36. 3(b)(i)6 marks· Mathematics Q3 3(b)(i)Calculate, giving reasons for your answers, the size of angle ABC.
37. 3(b)(i)a)4 marks· Mathematics Q3 3(b)(i)a)Calculate, giving a reason for your answer, the measure of ∠ BAC.
38. 3(b)(i)b)4 marks· Mathematics Q3 3(b)(i)b)Calculate, giving a reason for your answer, the measure of ∠ AED.
39. 3(b)(ii)6 marks· Mathematics Q3 3(b)(ii)Calculate, giving reasons for your answers, the size of angle ABD.
40. 3(b)(ii)2 marks· Mathematics Q3 3(b)(ii)Explain why triangles ABC and ADE are similar but not congruent.
41. 3(b)(ii)1 mark· Mathematics Q3 3(b)(ii)Explain why triangles ABC and ADE are similar.
42. 3(b)(iii)6 marks· Mathematics Q3 3(b)(iii)Calculate, giving reasons for your answers, the size of angle BAD.
43. 3(b)(iii)3 marks· Mathematics Q3 3(b)(iii)Determine the length of DE.
44. 4(b)(i)6 marks· Mathematics Q4 4(b)(i)Calculate ∠ZXV.
45. 4(b)(ii)6 marks· Mathematics Q4 4(b)(ii)Calculate ∠ZVX.
46. 4(b)(iii)7 marks· Mathematics Q4 4(b)(iii)Calculate correct to one decimal place the size of the angle HDE.
47. 4(b)(iii)2 marks· Mathematics Q4 4(b)(iii)On the diagram, show the point, K, such that KLMN is a parallelogram.
48. 5(a)(i)2 marks· Mathematics Q5 5(a)(i)Determine, giving a reason for each step of your answer, the measure of angle RQT.
49. 5(a)(i)2 marks· Mathematics Q5 5(a)(i)Determine, giving reasons for EACH of your answers, the value of x.
50. 5(a)(i)2 marks· Mathematics Q5 5(a)(i)Complete the following statement: In the diagram above, the corresponding angles of Δ PQR and Δ STR are __________ and the __________ of their corresponding sides are the same.
51. 5(a)(i)4 marks· Mathematics Q5 5(a)(i)Calculate, giving reasons for your answers, the measure of ∠ MLP.
52. 5(a)(ii)4 marks· Mathematics Q5 5(a)(ii)Calculate, giving reasons for your answers, the measure of ∠ LJK.
53. 5(a)(ii)3 marks· Mathematics Q5 5(a)(ii)Determine the length of PQ.
54. 5(a)(ii)2 marks· Mathematics Q5 5(a)(ii)Determine, giving a reason for each step of your answer, the measure of angle PRT.
55. 5(a)(ii)2 marks· Mathematics Q5 5(a)(ii)Determine, giving reasons for EACH of your answers, the value of y.
56. 5(a)(iii)2 marks· Mathematics Q5 5(a)(iii)Determine, giving a reason for each step of your answer, the measure of angle SPT, given that angle SRT = 145° and angle PSR = 100°.
57. 5(a)(iii)2 marks· Mathematics Q5 5(a)(iii)Determine, giving reasons for EACH of your answers, the value of w.
58. 5(a)(iii)4 marks· Mathematics Q5 5(a)(iii)Calculate, giving reasons for your answers, the measure of ∠ JKL.
59. 5(a)(iii)2 marks· Mathematics Q5 5(a)(iii)Determine the size of each interior angle of the polygon.
60. 5(a)(iv)4 marks· Mathematics Q5 5(a)(iv)Calculate, giving reasons for your answers, the measure of ∠ KLJ.
61. 6(a)(i)2 marks· Mathematics Q6 6(a)(i)Calculate, giving reasons for your answer, the value of x.
62. 6(a)(i)2 marks· Mathematics Q6 6(a)(i)Determine, giving a reason for EACH of your answers, the value of x
63. 6(a)(i)4 marks· Mathematics Q6 6(a)(i)Calculate the size of the angle marked x°. Show all steps in your calculations and give reasons for your answers.
64. 6(a)(ii)1 mark· Mathematics Q6 6(a)(ii)Calculate the size of the angle marked y°. Show all steps in your calculations and give reasons for your answers.
65. 6(a)(ii)2 marks· Mathematics Q6 6(a)(ii)Determine, giving a reason for EACH of your answers, the value of y.
66. 6(a)(ii)2 marks· Mathematics Q6 6(a)(ii)Calculate, giving reasons for your answer, the value of y.
67. 6(a)(iii)2 marks· Mathematics Q6 6(a)(iii)Calculate, giving reasons for your answer, the value of z.
68. 6(b)(ii)1 mark· Mathematics Q6 6(b)(ii)Determine the value of angle PNM.
69. 10(a)(i)2 marks· Mathematics Q10 10(a)(i)Determine the size of angle AOB.
70. 10(b)(ii)1 mark· Mathematics Q10 10(b)(ii)Calculate the measure of ∠KLM.
71. 10(b)(ii)a)1 mark· Mathematics Q10 10(b)(ii)a)Name the triangle in the diagram which is congruent to triangle ZOU.
72. 10(b)(ii)b)1 mark· Mathematics Q10 10(b)(ii)b)Name the triangle in the diagram which is congruent to triangle YXU.
73. 10(b)(iv)2 marks· Mathematics Q10 10(b)(iv)Complete the following statements: The size of the angle through which the wire moves from RP to RT is _____. An angle which is the same in size as RTV is _____.
74. 11(a)(ii)1 mark· Mathematics Q11 11(a)(ii)Calculate the area of triangle YXZ.
75. 11(b)3 marks· Mathematics Q11 11(b)Show that ΔBCE and ΔADE are similar.
76. 11(b)(i)11 marks· Mathematics Q11 11(b)(i)Calculate, giving your answer correct to 2 decimal places, the radius of the circle.
77. 11(b)(i)(a)3 marks· Mathematics Q11 11(b)(i)(a)Calculate the size of angle SJM.
78. 11(b)(i)(b)1 mark· Mathematics Q11 11(b)(i)(b)Calculate the size of angle JKM.
79. 11(c)(i)3 marks· Mathematics Q11 11(c)(i)Calculate the length of EB.
80. 12(a)(i)6 marks· Mathematics Q12 12(a)(i)Calculate the size of angle YXZ.
81. 12(a)(i)6 marks· Mathematics Q12 12(a)(i)Sketch the diagram and label the equator.
82. 12(a)(i)a)2 marks· Mathematics Q12 12(a)(i)a)Copy the sketch and label the arc which represents 60°N.
83. 12(a)(i)b)2 marks· Mathematics Q12 12(a)(i)b)Copy the sketch and label the arc which represents 35°E.
84. 12(a)(ii)6 marks· Mathematics Q12 12(a)(ii)Sketch the diagram and label the Greenwich Meridian.
85. 12(a)(ii)a)2 marks· Mathematics Q12 12(a)(ii)a)Copy the sketch and insert the point J (60°N, 35°E).
86. 12(a)(ii)b)2 marks· Mathematics Q12 12(a)(ii)b)Copy the sketch and insert the point K (60°N, 15°W).
87. 12(a)(iii)6 marks· Mathematics Q12 12(a)(iii)Sketch the diagram and label latitude 52°N.
88. 12(a)(iv)6 marks· Mathematics Q12 12(a)(iv)Sketch the diagram and label latitude 6°N.
89. 12(b)(i)3 marks· Mathematics Q12 12(b)(i)Copy the diagram and a) label the arc which represents 25°W b) draw an arc to represent the circle of latitude 60°N.
90. 12(b)(i)2 marks· Mathematics Q12 12(b)(i)Show on your diagram the position, L, of London and A, of Accra.
91. 12(b)(i)a)2 marks· Mathematics Q12 12(b)(i)a)Copy the sketch above, and draw and label two arcs to represent the Equator
92. 12(b)(i)b)1 mark· Mathematics Q12 12(b)(i)b)Copy the sketch above, and draw and label two arcs to represent the Greenwich Meridian.
93. 12(b)(ii)2 marks· Mathematics Q12 12(b)(ii)On your diagram, show the points a) R (60°N, 25°W) b) T (60°N, 40°E).
94. 12(b)(ii)a)2 marks· Mathematics Q12 12(b)(ii)a)Insert the points Y and M on your diagram.
95. 12(c)(i)1 mark· Mathematics Q12 12(c)(i)Show on your diagram a possible point of location of Kyle, K.
96. 13(a)(i)1 mark· Mathematics Q13 13(a)(i)Make a sketch of the diagram and show the points P and Q.