IGCSEMaths: CoreCIEExam QuestionsGeometryAngles in Polygons & Parallel Lines

Syllabus Edition

First teaching 2021

Last exams 2024

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Angles in Polygons & Parallel Lines (CIE IGCSE Maths: Core)

Exam Questions

2 hours32 questions
Easy
Medium
Hard
1
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Work out the size of one interior angle of a regular 16-sided polygon.

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2
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qp5-0580-11-paper-1-may-2020-cie-igcse-maths

In the triangle A B C comma space A B space equals space A C and angle B A C space equals space 38 degree.

B C D spaceis a straight line.

Work out angle A C D.

Angle A C D = ..................................................

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3
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Work out the size of one interior angle of a regular 9-sided polygon.

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4
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i)
Write down the mathematical name for an 8-sided polygon.
[1]
ii)
Work out the size of an interior angle of a regular 24-sided polygon.
[2]

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5
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Find the size of one interior angle of a regular octagon.

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6a
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q8-058012-mayjune2019-cie-igcse-maths-core

The diagram shows two parallel lines and a straight line crossing them.

Write down, using letters from a to g,

the angle that is alternate to angle X,

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6b
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the angle that is corresponding to angle X.

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7
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Calculate the size of one exterior angle of a regular 15-sided polygon.

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8
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Work out the size of one interior angle of a regular hexagon.

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1
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qp10-0580-12-paper-1-nov-2020-cie-igcse-maths

The diagram shows a triangle drawn between a pair of parallel lines.

Find the value of x and the value of y.

x space equals space.............................. y space equals space..............................

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2
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A regular polygon has an exterior angle of 20°.

Work out the number of sides of this polygon.

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3
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qp8b-0580-33-paper-3-nov-2020-cie-igcse-maths

The diagram shows two parallel lines and two straight lines.

i)
Find the value of a.
Give a reason for your answer.
a = ................ because ........................................................................................................... [2]
ii)
Find the value of b.
Give a reason for your answer.
b = ................ because .......................................................................................................[2]
iii)
Find the value of c.
c = ................................................. [2]

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4a
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qp8-0580-13-paper-1-may-2020-cie-igcse-maths

In the diagram, A B is parallel to C D.

Find the value ofspace x.
Give a geometrical reason for your answer.

x= ......................... because ....................................

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4b
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Work out the value of y.
Give a geometrical reason for your answer.

y space equals.................because ......................

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5
Sme Calculator2 marks

qp8a-0580-03-paper-3-specimen-2020-cie-igcse-maths

Work out the value of

i)
x comma
x=..........................[1]
ii)
y.
y space equals...........................[1]

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6
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Find the size of one interior angle of a regular 10-sided polygon.

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7a
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A triangle is isosceles.
One of its angles is 96°.

Find the other two angles.

........................ and ........................

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7b
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q7b-058032-mayjune2019-cie-igcse-maths-core

Find the value of x.

x = ...................................................

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7c
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Work out the size of one interior angle of a regular polygon with 20 sides.

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7d
Sme Calculator2 marks

q7d-058032-mayjune2019-cie-igcse-maths-core

The diagram shows a right-angled triangle A B C.
Calculate the length of A B.

A B = ................................................m

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8
Sme Calculator4 marks

q22-058011-octnov2018-cie-igcse-maths-core

The diagram shows an isosceles triangle A B C with A B space equals space A C.
L C M and B C N are straight lines and L C M is parallel to A B.
Angle A C L space equals space 56 degree.
Find the value of space x spaceand the value of y.

x = ................................. 
y = ................................. 

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9
Sme Calculator3 marks

Work out the size of an interior angle of a regular 20-sided polygon.

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10
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Work out the size of one exterior angle of a regular octagon.

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11
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Find the size of one interior angle of a regular decagon.

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1
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qp7b-0580-31-paper-3-nov-2020-cie-igcse-maths

A B C D is a rectangle.
A E is parallel to D B F.

Find the value of x and the value of y.

x = ................................................
y = .................................................

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2
Sme Calculator3 marks

qp7d-0580-31-paper-3-nov-2020-cie-igcse-maths

Two regular octagons and a square meet at point P.
Show, by calculation, that the three interior angles at P add up to 360°.

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3
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qp7b-0580-32-paper-3-may-2020-cie-igcse-maths

The diagram shows two pairs of parallel lines.

Find the value of a, the value of b and the value of c.

a space equals space................................................. space b space equals space................................................. space c space equals space................................................. space

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4
Sme Calculator4 marks

The diagram shows part of a different regular polygon.

qp7b-0580-33-paper-3-may-2020-cie-igcse-maths

e is an exterior angle.
i is an interior angle.
The ratio e space colon space i equals 2 colon 13.

i)
Work out angle e.
[3]

ii)
Work out the number of sides of this regular polygon.
[1]

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5
Sme Calculator1 mark

qp13-0580-01-paper-1-specimen-2020-cie-igcse-maths

A B C D E is a pentagon.

Explain why the diagram shows that the sum of the interior angles of a pentagon is 540°.
Do not measure any angles.

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6
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The diagram shows a triangle between two parallel lines, A B and C D.

qp7b-0580-33-paper-3-oct-nov-2019-cie-igcse-maths

Find the value of

i)
v comma
v=....................................[1]
ii)
w comma
w equals.............................[1]
iii)
y.
y = ................................................... [1]

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7
Sme Calculator2 marks

q4d-058031-mayjune2019-cie-igcse-maths-core

In the diagram space A G spaceand A F are straight lines.
Lines B C and D E are parallel.

Find angle C E D and give a reason for your answer.

Angle C E D = ................................. because ...................................

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8
Sme Calculator4 marks

q23-058013-mayjune2019-cie-igcse-maths-core

The diagram shows two regular pentagons.
Pentagon F G H J K is an enlargement of pentagon A B C D E, centre O.

Find angle A E K.

Angle A E K = .............................. 

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9
Sme Calculator8 marks

q6a-058033-mayjune2019-cie-igcse-maths-core

In the diagram, A B C is a straight line.
A D is parallel to B E, angle B A D = 34° and A B space equals space B D.

i)
Complete the statements.

a)
p space equals ................ because ................................

[2]

b)
q space equals ................ because .................................
[2]
ii)
Work out the value of r and the value of s.

r space equals space....................     
s space equals .................... [2]

iii)
Find the value of t and give a reason for your answer.

t space equals................ because ........................

[2]

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10
Sme Calculator3 marks

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.

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11
Sme Calculator2 marks

q7-058011-mayjune2018-cie-igcse-maths-core

The diagram shows two parallel lines P A Q and S B C T.
A B space equals space A C and angle Q A C space equals space 43 degree.

Find the value of x.

x space equals ............................. 

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12
Sme Calculator9 marks

q8b-058032-mayjune2018-cie-igcse-maths-core

The diagram shows a circle, centre F and diameter B G.
A C is a tangent to the circle at B.
B F is parallel to D E, angle G F E space equals space 72 degree and angle B C D = angle C D E.

i)
Write down the mathematical name of the polygon B C D E F.

[1]

ii)
Explain why angle F B C is a right angle.

[1]

iii)
Find angle B F E, giving a reason for your answer.

Angle B F E =....................... because ....................... [2]

iv)
Find angle F E D.
Angle F E D = ........................... [1]
v)
Calculate angle B C D.
Angle B C D = ............................ [4]

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13
Sme Calculator4 marks

q20-058012-march2018-cie-igcse-maths-core

Complete the statements.

a space equals ............................ because ............................ 

b space equals ........................... because ............................ 

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