Angles in Polygons & Parallel Lines (Cambridge (CIE) IGCSE Maths: Core): Exam Questions

Exam code: 0580 & 0980

1 hour26 questions
1
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2 marks

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

2
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2 marks

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

3
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1 mark

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]

4
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3 marks

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

5a1 mark
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,

5b1 mark

the angle that is corresponding to angle X.

6
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3 marks

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

7
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3 marks

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

1
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3 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..............................

2
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1 mark

A regular polygon has an exterior angle of 20°.

Work out the number of sides of this polygon.

3
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6 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]

4a2 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 ....................................

4b
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2 marks

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

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

5
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2 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]

6
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3 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]

7
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4 marks
q20-058012-march2018-cie-igcse-maths-core

Complete the statements.

a space equals ............................ because ............................   

b space equals ........................... because ............................ 

1
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2 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 = ................................................. .....

2
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3 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°.

3
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3 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

4
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4 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]

51 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.

62 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 ...................................

7
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4 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 = .............................. 

8
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8 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]

9
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3 marks

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.

10a
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3 marks

A model of a hall in the shape of a trapezium is made by joining together three equilateral triangles.

Dark grey trapezium with a black outline, divided into two triangles by a diagonal line from the top centre to the bottom right corner, on a white background.

The perimeter of one of the triangles is 72 cm.

Work out the perimeter of the trapezium.

10b1 mark

The trapezium model from part (a) is duplicated, with the copy being rotated and attached along the bottom of the original trapezium, making a regular polygon.

A polygon with 6 sides divided into six equal triangular segments, shaded in dark grey, with black outlines on a white background.

Give the name of this regular polygon.

10c
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2 marks

Calculate the exterior angle, x, of the polygon in part (b).

10d
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1 mark

Work out the interior angle, y,of the polygon in part (b).

11
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4 marks
Intersecting lines with labelled points A to H. Angles are marked: angle D is 54 degrees, and angle F is 31 degrees.

In the diagram, A I and E H are straight lines.

Lines B D and F G are parallel.

Find the angle D C G.

12
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2 marks

Show that the sum of the interior angles in a hexagon is 720 degree.