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
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Calculate the size of one interior angle of a regular polygon with 40 sides.

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2
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Find the interior angle of a regular polygon with 24 sides.

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3
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cie-igcse-20219-oct-nov-1-q1a

In the diagram, AC and BD are straight lines.

Find the value of p and the value of q.

p = ...................................................     

q = ...................................................     

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1
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cie-igcse-2019-may-jun-p4-tz2-q2a

A C is parallel to F B D, A B C is an isosceles triangle and C B E is a straight line.

Find the value of x. 
 

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

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2a
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cie-igcse-2019-may-jun-p2-tz3-q25a

The diagram shows two regular pentagons.
Pentagon space 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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2b
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The area of pentagon F G H J K is 73.5 space text cm end text squared.
The area of pentagon A B C D E is 6 space text cm end text squared.

Find the ratio    perimeter of pentagon F G H J K : perimeter of pentagon A B C D E    in its simplest form.
 

......................... : .........................

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3
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In a regular polygon, the interior angle is 11 times the exterior angle.

i)
Work out the number of sides of this polygon.

[3]
ii)
Find the sum of the interior angles of this polygon.

[2]

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

A B C D is a parallelogram.

Angle A D B space equals space 38 degree.
Angle B E C space equals space 41 degree.
Angle D A B space equals space 120 degree.

Calculate the size of angle x.
You must give reasons for your answer.

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1
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The interior angle of a regular polygon with n sides is 150°.
 
Calculate the value of n.
 

n equals................................................

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2
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A regular polygon has 72 sides.

Find the size of an interior angle.

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3
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cie-igcse-2018-may-jun-1-5

The diagram shows two parallel lines PAQ and SBCT.

AB = AC and angle QAC = 43°.

Find the value of x.


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

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1
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The diagram shows a triangle and a quadrilateral. All angles are in degrees.

cie-igcse-2019-oct-nov-p4-tz3-q2a

i)

For the triangle, show that  3 a plus 5 b equals 170.

[1]

ii)
For the quadrilateral, show that  9 a plus 7 b equals 310.

 

[1]

iii)
Solve these simultaneous equations.
Show all your working.

 

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

b = ................................................... [3]

iv)

Find the size of the smallest angle in the triangle.


[1]

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2a
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Show that each interior angle of a regular pentagon is 108 degree. 

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2b
Sme Calculator9 marks

cie-igcse-2019-may-jun-p4-tz2-q7b

The diagram shows a regular pentagon A B C D E.
The vertices of the pentagon lie on a circle, centre O, radius 12 space text cm end text.
M is the midpoint of B C.

i)
Find B M.
 
B M = ........................................ cm [3]

O M X and A B X are straight lines.

iia)
Find B X. 
 
B X = ........................................ cm [3]
iib)
Calculate the area of triangle A O X. 
 
........................................ cm2 [3]

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3
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The diagram shows a regular 10-sided polygon, A B C D E F G H I J

q11-4ma1-2h-qp-jan22-paper2-igcse-maths

Show that x space equals space y.

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