IGCSEMaths: CoreCIETopic QuestionsGeometryBasic Angle Properties

Syllabus Edition

First teaching 2023

First exams 2025

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Basic Angle Properties (CIE IGCSE Maths: Core)

Topic Questions

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1
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qp11-0580-13-paper-1-may-2020-cie-igcse-maths-1

Triangle A B C is isosceles.
Angle A B C = 32° and A B space equals space A C.

Find angle B A C.

Angle B A C = ................................................. 

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2
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qp4-0580-12-paper-1-march-2020-cie-igcse-maths

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

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

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3
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A student measures the angles in a triangle as 55°, 85° and 50°.

Explain why the student is incorrect.

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4
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qp7a-0580-32-paper-3-may-2020-cie-igcse-maths

The diagram shows an isosceles triangle.

Find the value of x.

x space= ................................................. 

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5
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A B C is a straight line.

qp3b-0580-31-paper-3-oct-nov-2019-cie-igcse-maths

Find the value of y.

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

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1
Sme Calculator3 marks

The diagram shows a trapezium.

qp14-0580-11-paper-1-may-2020-cie-igcse-maths

Work out the value of x.

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

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2
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Kim knows that one angle of an isosceles triangle is 48°.
He says that one of the other angles must be 66°.

Explain why Kim is wrong.

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3
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qp5b-0580-32-paper-3-oct-nov-2019-cie-igcse-maths

The diagram shows triangle P R S and a straight line Q S.
Q is a point on P R.
Angle Q R S = 25°, angle R S Q = 32° and P S space equals space Q S.

i)
Find angle P Q S.
Angle P Q S = ................................................... [2]
ii)
Find angle P S R.
Angle P S R = ................................................... [2]

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4
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The diagram shows a triangle.

q8e-058031-octnov2018-cie-igcse-maths-core

Use the diagram to write down an equation and solve it to find the value of x.

x = .................................. [4]

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5
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q5d-058032-octnov2018-cie-igcse-maths-core

The diagram shows an isosceles triangle, A B C.
B C D is a straight line.

Find the value of x.

x space equals ................................ [2]

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1
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qp7a-0580-31-paper-3-nov-2020-cie-igcse-maths

The diagram shows an isosceles triangle and a straight line.
Work out the value of w.

w equals...............................[2]

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2
Sme Calculator3 marks

qp8b-0580-03-paper-3-specimen-2020-cie-igcse-maths

Work out the value of w.
Give reasons for your answer.

w space equals ............................ because ....................................................................................................

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3
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Q R S spaceis an isosceles triangle and P Q R is a straight line.

qp3c-0580-31-paper-3-oct-nov-2019-cie-igcse-maths

Find the value of z.

z = ................................................... 

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4
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q4a-058031-mayjune2019-cie-igcse-maths-core

A B C is an isosceles triangle.
B C D is a straight line.

Find the value of a.

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

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5
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qp2c-0580-32-paper-3-nov-2020-cie-igcse-maths

A B C spaceis a straight line and BCD{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true} is an isosceles triangle.
Find the value of x{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}.

x {"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}= ................................................. 

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6
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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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7a
Sme Calculator1 mark

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

Find the other two angles.

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

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7b
Sme Calculator4 marks

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

Find the value of x.

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

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