IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.2 Angles in Polygons & Parallel Lines

Syllabus Edition

First teaching 2021

Last exams 2024

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

Topic Questions

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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 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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4
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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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5
Sme Calculator5 marks

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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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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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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3
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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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4
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A regular polygon has 72 sides.

Find the size of an interior angle.

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5
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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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1a
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Show that each interior angle of a regular pentagon is 108 degree. 

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1b
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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2
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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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3
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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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4
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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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5
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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