41 P6.AN.NK.17050202
Level 3
In the figure, not drawn to scale, O is the centre of the semi circle and OABC is a rhombus. ∠OCD = 32°. Find
  1. ∠x
  2. ∠y.
3 m
Isosceles triangle Circle Rhombus Corresponding angles Interior angles
42 P6.AN.NK.17081702
Level 3 PSLE
In the figure, WXYZ is a parallelogram and YZRS is a rhombus. ∠XYS = 90° and ∠YSZ = 24°. Find ∠WXY.
3 m
Isosceles triangle Parallelogram Rhombus Angles sum of triangle Angles at a point Interior angles
43 P6.AN.NK.17051727
Level 3
In the figure, not drawn to scale, ACDE is a parallelogram and ABF is an isosceles triangle. EFCB is a straight line. ∠CDE = 100°, ∠ACF = 54° and ∠CAB = 12°. Find ∠EAF.
3 m
Isosceles triangle Parallelogram Angles on a straight line Exterior angle of a triangle Alternate angles Interior angles
44 P6.AP.TL.17090781
Level 3
The figure is formed by a circle and an isosceles triangle XYZ. The diameter of the circle is 56 cm. Find the difference in area between the two shaded parts. (Take π = 227)
3 m
Isosceles triangle Semicircle Circle area
45 P6.AN.NK.17051722
Level 3
In the figure, not drawn to scale, JKL is an isosceles triangle, KLMN is a parallelogram and NKJ is a straight line. Find ∠NQP.
3 m
Isosceles triangle Parallelogram Angles on a straight line Interior angles Sum of angles in a quadrilateral
46 P6.AN.NK.17050203
Level 3
In the figure, not drawn to scale, WY, XZ and OX are straight lines. Given that O is the centre of the circle and ∠OWZ = 31°, find ∠OYZ.
3 m
Isosceles triangle Angles on a straight line Angles sum of a triangle Angle properties within a circle
47 P6.AN.NK.17050204
Level 3
In the figure, not drawn to scale, O is the centre of the circle. HOC, FDC and ODE are straight lines. Find ∠EDF.
3 m
Isosceles triangle Vertically opposite angles Angles at a point Corresponding angles Angle properties within a circle
48 P6.AP.TL.17090794
Level 3
The figure consists of a rectangle, a quadrant and an isosceles triangle. Given that the radius of the quadrant is 10 cm and B is the midpoint of Line AC, find the difference between the shaded areas Y and Z. Express the answer in nearest whole number. (Take π = 3.14)
3 m
Rectangle Isosceles triangle Quarter circle Composite figure area W Round off
49 P6.AN.NK.17050205
Level 3
In the figure, ABCD is a parallelogram and C is the centre of the circle. Find ∠BCE.
3 m
Isosceles triangle Parallelogram Angles sum of triangle Interior angles Angle properties within a circle
50 P6.AP.TL.17090805
Level 3
The figure is made up of a right-angled isosceles triangle XYZ and a semicircle. XY = YZ and the diameter of the semicircle is 28 cm. Find the area of the shaded part of the figure.
3 m
Isosceles triangle Right-angled triangle Semicircle Composite figure area Cut & paste
51 P6.AN.NK.17051721
Level 3
The figure is not drawn to scale. UVY is an equilateral triangle and XVW is an isosceles triangle. WVU and VXZ are straight lines and WU//ZY. ∠YVZ = 90° and ∠XYV = 56°.
  1. Find ∠WVZ.
  2. Find ∠VXW.
  3. Find ∠YXZ.
4 m
Equilateral triangle Isosceles triangle Angles on a straight line
52 P6.AN.NK.17051740
Level 3
The figure is not drawn to scale. BCEF is a square and ABF is an equilateral triangle. CDE is an isosceles triangle. AED is a straight line.
  1. Find ∠FAE.
  2. Find ∠CDE.
4 m
Square Equilateral triangle Isosceles triangle Angles on a straight line
53 P6.AN.NK.17051701
Level 3
The figure is not drawn to scale. Triangle ABZ is an isosceles triangle. Triangle XYZ is an equilateral triangle. ∠BZA is 15 of ∠YXZ and ∠YZB = ∠XZA.
  1. Find ∠YZB.
  2. Find ∠XAZ.
4 m
Equilateral triangle Isosceles triangle Angles sum of triangle Fraction of a whole
54 P6.AN.NK.17051731
Level 3
The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠c = ∠b, ∠a is twice ∠d, ∠b is twice ∠e and ∠c is less than ∠e by 51°.
  1. Find ∠c.
  2. Find the difference between ∠a and ∠c.
4 m
Isosceles triangle Rhombus Angles sum of triangle More than or less than Times as many Units
55 P6.AN.NK.21060916
Level 3 PSLE
In the figure, ABFG is a parallelogram and CDEF is a rhombus. GFE is a straight line. ∠BAG = 53°, ∠FBC = 27° and ∠DCE = 35°.
  1. Find ∠BFC.
  2. Find ∠BCD.
4 m
Isosceles triangle Parallelogram Rhombus Angles on a straight line Angles sum of triangle Angles at a point
56 P6.AN.NK.17050208
Level 3
In the figure, not drawn to scale, O is the centre of the circle. Given that the ratio of ∠OBC : ∠AOC is 3 : 11. Find ∠AOB.
4 m
Isosceles triangle Circle Angles at a point Ratio to units Units method
57 P6.AN.NK.21060926
Level 3 PSLE
ABCD is a rhombus. DFB and DECG are straight lines.
  1. Find ∠ABD.
  2. Find ∠DCG.
  3. Find ∠DFE.
4 m
Isosceles triangle Rhombus Angles on a straight line Angles sum of triangle Exterior angle of a triangle
58 P6.AN.NK.21060912
Level 3 PSLE
In the figure, ABCD is a straight line, BDEF is a parallelogram and EC = EF. ∠FAB is a right angle, ∠AFB = 30° and ∠DEC = 20°.
  1. Find ∠x.
  2. Find ∠y.
4 m
Right angle Isosceles triangle Parallelogram Exterior angle of a triangle
59 P6.AN.NK.17050211
Level 3
In the figure, not drawn to scale, O is the centre of the smaller circle. AB is a straight line. Find ∠AED.
4 m
Isosceles triangle Circle Angles on a straight line Alternate angles
60 P6.AN.JC.23031305
Level 3 PSLE
ABCD is a parallelogram, ACE is an equilateral triangle and DC = DE.
  1. Find ∠ACD.
  2. Find ∠CDA.
  3. Find &angEAB.
4 m
Isosceles triangle Equilateral triangle Parallelogram Angles sum of triangle Angles at a point Alternate angles

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