IGCSEMaths: CoreCIEExam QuestionsGeometryAngles in Polygons & Parallel Lines

Syllabus Edition

First teaching 2023

First exams 2025

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

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3
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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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4
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Find the size of one interior angle of a regular octagon.

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5a
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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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5b
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the angle that is corresponding to angle X.

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

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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
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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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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 Calculator4 marks

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

Complete the statements.

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

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

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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
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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
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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
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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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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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7
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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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8
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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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9
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Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.

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