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1 MTHEMTICS-1 asic Geometrical Concepts and Properties Page 1 of 15
2 FFC GRMMR SCHOOL GOTH MCHHI Chapter 14 asic Geometrical Concepts and Properties 1. In the figure, PQ is parallel to RS, PT is the bisector of R Pˆ Q and RT is the bisector of P Rˆ S. If P Rˆ T = and T Pˆ Q = y, what is the size of PTˆ R? (I) 90 (II) + y (III) 180 y () I only () I and II only (C) I and III only (D) II and III only (E) I, II and III ( ) 2. In the figure, OQ and PO are straight lines. Â = 35, ˆ = 40, Pˆ = 38 and Qˆ =. Find the value of x. () 21 () 37 (C) 43 (D) 49 (E) 67 ( ) Page 2 of 15
3 3. In the figure, // DE, ˆ C = 40, Ĉ D = and C Dˆ E = 115. What is the value of x? () 105 () 115 (C) 125 (D) 130 (E) 145 ( ) 4. In the diagram, is parallel to CD. The value of x is. () 138 () 124 (C) 118 (D) 108 (E) 62 ( ) 5. In the diagram, ˆ K and C ˆ K are complementary. Given that C ˆ K is 50 greater than ˆ K, the value of ˆ K in degrees is. () 20 () 40 (C) 45 (D) 50 (E) 60 ( ) 6. In the figure, // CD, Kˆ D =. ˆ K = 66 and C Dˆ K = 44. The value of x is. () 44 () 55 (C) 66 (D) 70 (E) 110 ( ) Page 3 of 15
4 7. In the figure, // CD, $ K = 140. $ K C = 82 and K $ C D = x. The value of x is. () 4 () 42 (C) 48 (D) 62 (E) 82 ( ) 8. The three straight lines, PQ and RS are parallel. Find the value of x. () 120 () 130 (C) 140 (D) 150 (E) 160 ( ) nswers 1. E C E C Page 4 of 15
5 Chapter 14 asic Geometrical Concepts and Properties 1. (a) What is the complement of the angle 52? [1] (b) What is the supplement of the angle 65? [1] 2. Form an equation in x and find x. [2] Given that O and FOD are straight lines and EOC = 90, OC = 22, EOD = 3 and OF = 4, find (a) x, [3] (b) COD, [1] (c) OE. [1] E D 3 C 22 O 4 F Page 5 of 15
6 4. In the diagram O and POQ are straight lines. OX = 42, OY = 24, POX = 4 and QOY = 6. Find (a) x, [2] X P 4x (b) PO. [2] O 6x Y Q 5. Find the values of x and y in the diagram. [4] 2 3 y 69 (4x+12) 6. In the figure, // PQ. Find the value of x. [2] Q (3x - 5) (x + 9) P Page 6 of 15
7 7. In the figure, POT, O, PQR and SOQ are straight lines. Given that O // PQR, OPQ = 90 and PQS = 42, calculate (a) OS, [2] (b) SOT, [1] (c) OQR. [1] S T O 42 P Q R 8. Given that C // PQ, find the value of x. [2] D 41 C P 79 Q 9. Find the value of x in the figure. [3] 3x-18 5x Find x in the given figure. [2] 7x Page 7 of 15
8 11. Find the value of x in the given figure. [3] Given that // PQ, find the value of x. [3] P 58 C 29 Q 13. Given that // DE, CD = 88 and CDE = 28, C =, find x. [3] C E D 14. Find the value of y in the given figure. [3] 52 2y Find the value of x in the given figure. [3] Page 8 of 15
9 16. Find the values of x and y in the given figure. [3] 79 y In the figure, // PQ. Find the value of y. [3] 127 y P 148 Q 18. In the figure, PQ //. Find the value of x. [2] P Q 79 C Form an equation in x and solve for x. [3] Form an equation in x and solve for x. [3] Page 9 of 15
10 21. In the figure, // DE. Find the value of y. [3] E y 126 C D 22. In the diagram, PQ //. Find the value of x. [3] Q P 23. Find the values of x and y in the diagram. [3] y 24. Find the values of x and y. [4] C D y 25. In the figure, // PQR. Find the value of x. [3] P Q R Page 10 of 15
11 26. Find the values of x and y in the given figure. [4] y 76 C D E 308 F 27. Find the value of x in the given figure. [4] Find the value of x in the given figure. [3] Find the values of x and y. [4] 4 64 y 3 Page 11 of 15
12 30. In the figure, // PQ // CD, $ C = 80, $ CP = y, P $ CD = and C $ PQ = 110. Find the values of x and y. [4] 31. In the figure, PQ // SR, P $ QS = 3, S $ QR = 40, Q $ RS = 4 and R $ S T = y. Find the values of x and y. [4] 32. Find the values of x and y given that is parallel to PQ. [4] 33. In the figure, C // DE. Find the values of x and y. [4] 34. In the figure, // QR. Find the value of x. [3] Page 12 of 15
13 35. Find the values of x and y in the figure. [4] 36. Find the values of x and y in the figure. [4] 37. In the given figure, find the value of x. [3] 38. In the diagram, // PQ. Find the value of x. [2] 39. In the given figure, PQ // RS. Find the value of x. [3] Page 13 of 15
14 nswers 1. (a) 38 (b) (a)16 (b) 42 (c) (a) 9 (b) x = 11, y = (a) 42 (b)48 (c) x = 49, y = Page 14 of 15
15 23. x = 47, y = x = 90, y = x = 52, y = x = 29, y = x = 70, y = x = 20, y = x = 39, y = x = 108, y = x = x = 72, y = x = 107, y = x = x = x = 57 Page 15 of 15
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