"Plane Geometry" question number distribution across years

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Mathematics index on skoool nigeria

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

**Answer:** C

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

**Answer:** B

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

**Answer:** A

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

**Answer:** C

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

**Answer:** B

Q7

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

A

128cm²

B

72cm²

C

64cm²

D

32cm²

E

**Answer:** D

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

**Answer:** B

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

**Answer:** B

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

**Answer:** D

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

**Answer:** A

Q12

Calculate the perpendicular distance between the parallel sides.

A

3.35cm

B

3.72cm

C

4.50cm

D

4.62cm

E

**Answer:** A

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

**Answer:** B

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

**Answer:** C

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

**Answer:** B

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

**Answer:** C

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

**Answer:** B

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

**Answer:** B

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

**Answer:** B

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

**Answer:** C

Q23

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

A

150°

B

120°

C

90°

D

60°

E

**Answer:** C

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

**Answer:** D

Q25

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

A

84°

B

48°

C

42°

D

32°

E

**Answer:** C

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

**Answer:** C

Q27

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

A

1:2

B

2:1

C

1:3

D

3:1

E

**Answer:** B

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

**Answer:** B

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

**Answer:** D

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

**Answer:** B

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

**Answer:** C

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

**Answer:** A

Q34

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

A

60°

B

80°

C

120°

D

160°

E

**Answer:** B

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

**Answer:** D

Q39

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

A

120°

B

110°

C

100°

D

80°

E

**Answer:** C

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

**Answer:** C

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

**Answer:** C

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

**Answer:** C

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

**Answer:** C

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

**Answer:** A

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

**Answer:** D

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

**Answer:** C

Q48

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

A

x² + 5x - 6 = 0

B

x² - 5x - 6 = 0

C

x² + x - 6 = 0

D

x² - x - 6 = 0

E

**Answer:** C

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

**Answer:** C

Q50

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

A

140m

B

220m

C

280m

D

440m

E

**Answer:** B

Q51

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

A

180° - z

B

180° + z

C

z -180°

D

z

E

**Answer:** A

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

**Answer:** D

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

**Answer:** A

Q54

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

A

13^{o}

B

17^{o}

C

28^{o}

D

30^{o}

E

**Answer:** B

Q55

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

A

95^{o}

B

100^{o}

C

120^{o}

D

150^{o}

E

**Answer:** D

Q56

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

A

40^{o}

B

50^{o}

C

55^{o}

D

75^{o}

E

**Answer:** C

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

**Answer:** B

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

**Answer:** A

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

**Answer:** D

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

**Answer:** B