IGCSEMaths: ExtendedCIETopic 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: Extended)

Topic Questions

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1
Sme Calculator3 marks

cie-igcse-2020-oct-nov-p2-tz2-q4

The diagram shows a triangle drawn between a pair of parallel lines.
Find the value of space x spaceand the value of y.


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

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

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2
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cie-igcse-2020-mary-jun-p2-tz3-q3

Triangle A B C is isosceles.
Angle A B C equals 32 degree and A B equals A C.
 
Find angle B A C.
 

Angle B A C equals................................................

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3
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cie-igcse-q8-angles-on-parallel-lines

Triangle ABC  is isosceles.
AC is parallel to BD.

Find the value of a and the value of b.


a = ..............................................       

b = ..............................................       

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1
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cie-igcse-2020-oct-nov-p4-tz1-q4b

ABDF is a parallelogram and BCDE  is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.

Explain why triangle CDF  is isosceles. 

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2
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cie-igcse-2020-oct-nov-p4-tz3-q5b

PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.

Explain why triangle PQR is similar to triangle PUT.
Give a reason for each statement you make.

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3
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The diagram shows a trapezium.

cie-igcse-2020-may-june-p2-tz1-q6

Work out the value of x.


x equals ..................................................

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4
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A hexagon has five angles that each measure 115°.

Calculate the size of the sixth angle.

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5
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The angles of a quadrilateral are x degree, left parenthesis x plus 5 right parenthesis degree, left parenthesis 2 x minus 25 right parenthesis degree and left parenthesis x plus 10 right parenthesis degree.

Find the value of x.

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

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6
Sme Calculator4 marks

cie-igcse-2018-oct-nov-p2-tz1-q16

The diagram shows an isosceles triangle ABC with AB = AC.
LCM and BCN are straight lines and LCM is parallel to AB.
Angle ACL = 56°.
 
Find the value of x and the value of y.
 

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

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1
Sme Calculator2 marks

The diagram shows two triangles, A B D and A D C.

q4-paper2-spec2025-cie-igcse-further-maths

B D C is a straight line, A B space equals space A C , angle A B D space equals space 61 degree and angle A D C space equals space 81 degree.
Work out angle D A C.

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

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2
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Find the number of sides of a regular polygon with interior angle 162°.

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3
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The interior angle of a regular polygon with n sides is 156 degree.

Work out the value of n.


n space equals ................................................

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4a
Sme Calculator1 mark

cie-igcse-2020-oct-nov-p2-tz3-q6

The diagram shows triangle ABC.
The triangle is reflected in the line BC to give a quadrilateral ABDC.

Write down the mathematical name of the quadrilateral ABDC.

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4b
Sme Calculator2 marks

Find angle ACD.
 

Angle ACD = ................................................

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5
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cie-igcse-2020-mary-jun-p2-tz2-q3

A B equals B C and A B D is a straight line.
 
Find the value of x.
 

x equals.................................................

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6
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A regular polygon has an interior angle of 176°.

Find the number of sides of this polygon.

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7
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The exterior angle of a regular polygon is x° and the interior angle is 8 x°.

Calculate the number of sides of the polygon.

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8
Sme Calculator4 marks

cie-igcse-2018-march-p2-15

Complete the statements.


a = ............................................... because ...............................................     
b = ............................................... because ...............................................     

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9
Sme Calculator3 marks

q5-4-2-easy-edexcel-gcse-maths

The diagram shows a regular octagon and a regular hexagon.

Find the size of the angle marked x.
You must show all your working.

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1
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q1-4-2-very-hard-edexcel-gcse-maths

The diagram shows a regular pentagon.
A B and C D are two of the lines of symmetry of the pentagon.

Work out the size of the angle marked x.
You must show all your working.

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2
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A B C D E F G H I is a regular 9-sided polygon.

q3-4-2-very-hard-edexcel-gcse-maths

The vertices B and E are joined with a straight line.

Work out the size of angle B E F.
You must show how you get your answer.

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3
Sme Calculator5 marks

q5-4-2-very-hard-edexcel-gcse-maths

P Q R S T is a regular pentagon.
R comma space U and T are points on a circle, centre O.
Q R and P T are tangents to the circle.
R S U is a straight line.

Prove that S T space equals space U T.

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