GCSEMathsEdexcelFoundationExam QuestionsGeometry & MeasuresAngles in Polygons & Parallel Lines

Angles in Polygons & Parallel Lines (Edexcel GCSE Maths: Foundation)

Exam Questions

2 hours40 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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6
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Work out the size of one interior angle of a regular 16-sided polygon.

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7
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Work out the size of one interior angle of a regular 9-sided polygon.

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8
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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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9
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Find the size of one interior angle of a regular octagon.

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10a
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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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10b
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the angle that is corresponding to angle X.

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11
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Find the size of one interior angle of a regular 10-sided polygon.

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12
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Work out the size of one interior angle of a regular polygon with 20 sides.

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1
Sme Calculator2 marks
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
Sme Calculator2 marks
qp2c-0580-32-paper-3-nov-2020-cie-igcse-maths

A B C spaceis a straight line and B C D is an isosceles triangle.
Find the value ofspace x.

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

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6
Sme Calculator3 marks
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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8
Sme Calculator3 marks
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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9
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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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10
Sme Calculator6 marks
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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11a
Sme Calculator2 marks
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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11b
Sme Calculator2 marks

Work out the value of y.
Give a geometrical reason for your answer.

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

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12
Sme Calculator2 marks
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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13
Sme Calculator3 marks

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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14
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
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
Sme Calculator2 marks

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
Sme Calculator4 marks
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
Sme Calculator4 marks

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
Sme Calculator2 marks
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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6
Sme Calculator2 marks
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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7
Sme Calculator3 marks
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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8
Sme Calculator3 marks
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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9
Sme Calculator4 marks

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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10
Sme Calculator1 mark
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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11
Sme Calculator2 marks
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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12
Sme Calculator4 marks
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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13
Sme Calculator8 marks
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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14
Sme Calculator3 marks

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.

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