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"Plane Geometry" question number distribution across years
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WAEC questions for "Mathematics :: Plane Geometry"
Q1

In the diagram, <PSR = 220°, <SPQ = 58° and <PQR = 41°. Calculate the obtuse angle QRS.

A

90°

B

100°

C

121°

D

165°

E
Q2

 In the diagram, QR//ST, /PQ/ = /PR/ and <PST = 75°. Find the value of y.

A

20°

B

30°

C

40°

D

50°

E
Q3

The sum of the exterior angles of an n-sided convex polygon is half the sum of its interior angles. find n.

A

6

B

8

C

9

D

12

E
Q4

In the diagram, QT??ST, /PQ/ = /PR/ and

A

105

B

110

C

130

D

150

E
Q5

In the diagram, the tangent MN makes an angle of 55° with the chord PS. If o is the centre of the circle, find <RPS.

A

55°

B

45°

C

35°

D

25°

E
Q6

In the diagram, O is the centre of the circle. <SQR = 60°, <SPR = y and <SOR = 3x. Find the value of (x + Y).

A

110°

B

100°

C

80°

D

70°

E
Q7

In the diagram, /EF/ = 8cm, /FG/ = xcm, /GH/ = (x+2)cm <EFG = 90°. If the area of the shaded portion is 40cm2, find the area of ΔFEG.

 

A

128cm²

B

72cm²

C

64cm²

D

32cm²

E
Q8

In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of <EHF.

A

126°

B

72°

C

54°

D

28°

E
Q9

In the diagram, <ROS = 66° and <POQ = 3x. Some construction lines are shown. Calculate the value of x. 

 

A

10°

B

11°

C

22°

D

30°

E
Q10

In the diagram, O is the centre of the circle. Find the value of x.

A

34

B

29

C

17

D

14

E
Q11

In the diagram,`<WOX = 60°, <YOE = 50° and <OXY = 30°. What is the bearing of x from y?

A

300°

B

240°

C

190°

D

150°

E
Q12

Calculate the perpendicular distance between the parallel sides.

A

3.35cm

B

3.72cm

C

4.50cm

D

4.62cm

E
Q13

In the diagram /TP/ = 12cm and it is 6cm from O, the centre of the circle. Calculate <TOP

A

120

B

90

C

60

D

45

E
Q14

The interior angles of a pentagon are (2x + 5), (x + 20), x, (3x - 20) and (x + 15). Find the value of x.

A

80

B

70

C

65

D

40

E
Q15

In the diagram IG is parallel to JE, <JEF = 120° and <FHG = 130° Find the angle marked t.  

A

40°

B

70°

C

80°

D

100°

E
Q16

If M and N are two fixed points in a plane, find the locus L = {P : PM = PN}.

A

A line equal to MN

B

A line parallel to MN

C

Perpendicular bisector of MN

D

A circle centre P, radius MN

E
Q17

Find the value of x in diagram.

A

50

B

30

C

22

D

17

E
Q18

In the diagram, angle 200 is subtended at the centre of the circle. Find the value of x.

A

30

B

50

C

80

D

100

E
Q19

each of interior angles of a regular polygon is 140. Calculate the sum of all the interior angles of the polygon.

A

1080

B

1260

C

1800

D

2160

E
Q20

From the diagram, which of then following statements is/are correct?

I. XQ is a radius of a circle Q.

II. /XQ/ = /QY/

III. /QX/ = /XY/

A

I only

B

I and II only

C

II and III only

D

I, II and III

E
Q21

Find the value of x in the diagram.

A

50

B

60

C

70

D

80

E
Q22

The angles of a triangle are (x + 10), (2x - 40) and (3x - 90). Which of the following accurately describes the triangle?

A

It is a scalene triangle

B

It ia right angled isosceles triangle

C

It is an equilateral triangle

D

It is an isosceles triangle but not right angled

E
Q23

In the diagram /PQ/ = /QR/ and /PR/ = /RS/ = /SP/. Calculate the side of <QRS

A

150

B

120

C

90

D

60

E
Q24

In the figure shown, PQS is a straight line. What is the value of <PRQ?

A

128

B

108

C

98

D

78

E
Q25

In the diagram, PQ//RS, QU//PT and <PSR = 42. Find angle x.

A

84

B

48

C

42

D

32

E
Q26

The anges of a quadrilateral are (x + 10), 2y, 90 and (100-y). Find y in term of x.

A

y = 160 + x

B

y = 100 + x

C

y = 160 - x

D

y = x - 100

E
Q27

In the figure /PX/ = /XQ/, PQ//YZ and XY//QR. What is the ratio of the area of XYZQ to the area of ΔYZR?

A

1:2

B

2:1

C

1:3

D

3:1

E
Q28

In the diagram, O is the center of the circle and PQRS is a cyclic quadrilateral. FInd the value of x.

A

25

B

65

C

115

D

130

E
Q29

If x is obtuse, which of the following is true?

A

x>90

B

180

C

x<90

D

90

E
Q30

An arc of a circle, radius 14cm, is 18.33cm long. Calculate, to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take π=22/7].

A

11

B

20

C

22

D

75

E
Q31

XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120 at the centre of the circle. Calculate the perimeter of the minor segment. [Take π = 22/7]

A

14.67cm

B

22.67cm

C

29.33cm

D

37.33cm

E
Q32

In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate <PTS

A

60

B

90

C

120

D

150

E
Q33

In the diagram, <QPR = 60°, <PQR = 50°, <QRS = 2x°, <SRP = 3x°, <UQP = y° and RS // TU. Calculate y.

A

102°

B

78°

C

70°

D

60°

E
Q34

In the diagram, find the size of the angle marked a.

A

60

B

80

C

120

D

160

E
Q35

From the diagram, find the value of x

A

80

B

70

C

55

D

35

E
Q36

Find the value of x in the diagram

A

281

B

269

C

201

D

179

E
Q37

Each interior angle of a regular polygon is 162. How many sides has the polygon

A

8

B

12

C

16

D

20

E
Q38

From the diagram, find the value of x.

A

40

B

30

C

25

D

20

E
Q39

In the diagram, |SP| = |SR| and <PRS = 50°. Calculate <PQR.

A

120°

B

110°

C

100°

D

80°

E
Q40

In the diagram, O is the cetre of the circle and <PQR = 106°. Find the value of y.

A

16

B

37

C

74

D

127

E
Q41

In a ΔPQR, <PQR = <PRQ = 45°. Which of the following statements is/are correct?

I.  ΔPQR is an equilateral triangle

II. ΔPQR ia an isosceles triangle

III.ΔPQR is a right-angled triangle

A

II only

B

I and II only

C

II and III only

D

I and III only

E
Q42

In the diagram, |XR| = 4cm, |RZ| = 12cm, |SR| = n, |YZ| = m and SR||YZ. Find m in terms of n

A

m = 2n

B

m = 3n

C

m = 4n

D

m = 5n

E
Q43

P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is

A

a straight line joining A and P

B

the perpendicular bisector of AP

C

a circle with centre A

D

the triangle with centre P

E
Q44

Which of these diagrams show(s) the correct method of constructing a perpendicular line to another line PQ ata given point X on PQ?

A

I only

B

II only

C

I and II only

D

I, II and III

E
Q45

In the diagram, |QR| = 5cm, <PQR = 60° and <PSR = 45°. Find |PS|, leaving your answer in surd form.

A

4√5 cm

B

3√7 cm

C

4√6 cm

D

5√6 cm

E
Q46

In the diagram, PQ//RS, find x + y

A

360

B

300

C

270

D

180

E
Q47

In the diagram, PR is a diagram of the circle centre O. RS ia a tangent at R and <QPR = 58°. Find <QRS.

A

112°

B

116°

C

122°

D

148°

E
Q48

Which of these equations best descibes the points of instersection of the curve and the line?

A

x + 5x - 6 = 0

B

x - 5x - 6 = 0

C

x + x - 6 = 0

D

x - x - 6 = 0

E
Q49

In the diagram, PQR is a straight line, QRST is a parallelogram, <TPQ =72° and <RST = 126°. What type of triangle is Δ PQT?

A

An equilateral triangle

B

A right-angled triangle

C

An isosceles triangle

D

A scalene triangle

E
Q50

The diagram shows an arc MN of a circle, centre O, with 10cm. If

A

140m

B

220m

C

280m

D

440m

E
Q51

In the diagram, what is x + y in terms of z?

A

180 - z

B

180 + z

C

z -180

D

z

E
Q52

The va;lues of three angles at a point are 3y - 45, y + 25 and y. Find the value of y.

A

40

B

58

C

68

D

76

E
Q53

In the diagram, KL//MN, <LKP = 30° and <NMP = 45°. Find the size of the reflex <KPM.

A

285°

B

255°

C

225°

D

210°

E
Q54

In the diagram, PQ and MN are straight lines. Find the value of x.

A

13o

B

17o

C

28o

D

30o

E
Q55

In the diagram, PQRS is a parallelogram and <QRT = 30°. Find x.

A

95o

B

100o

C

120o

D

150o

E
Q56

In the diagram, O is the centre of the circle, o , <LMO = 10o and <LNO = 15°. Calculate the value of x.

A

40o

B

50o

C

55o

D

75o

E
Q57

The figure shows a quadrilateral PQRS having equal sides and opposite sides parallel. The diagonals PQ and QS intersect perpendicularty at O, which of the following statement cannot be correct?

A

|PO| = |RO|

B

PQR is an equilateral traingle

C

PQRS is a parallelogram

D

There are two lines of symmetry

E
Q58

Which of the following statements describes the locus of a point R which moves in a plane such that it is equidistant from two intersecting lines?

A

The bisector of the angles formed by the lines

B

The point of intersection of the two lines

C

A cone, with the two intersecting lines as slant heights

D

A circle, with the point of inetrsection of the two lines as the center.

E
Q59

A regular polygon has 9 sides. What is the size of one of its exterior angles?

A

20

B

40

C

90

D

140

E
Q60

In the diagram PQRS is a circle, |PT|=|QT| and QPT = 70°. What is the size of <PRS.

A

40°

B

70°

C

80°

D

140°

E