Question 5 — IGCSE 0580 May/June 2024 Paper 31
Cambridge IGCSE Mathematics 0580, Core tier, calculator. Topic: Geometry · Angles using geometrical properties. Worth 13 marks.
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Question text
5 (a)
H F I
NOT TO
f °
105° SCALE
e° 52°
E G
The diagram shows a triangle EFG and a straight line HFI.
HFI is parallel to EG.
(i) Angle EFG = 105°.
Write down the mathematical name for this type of angle.
................................................. [1]
(ii) Work out the value of e.
Give a geometrical reason for your answer.
e = ......................... because ..............................................................................................
............................................................................................................................................. [2]
(iii) Find the value of f.
Give a geometrical reason for your answer.
f = ......................... because ..............................................................................................
............................................................................................................................................. [2]
(b) Calculate the interior angle of a regular 7-sided polygon.
Give your answer correct to 2 decimal places.
................................................. [3]
© UCLES 2024 0580/31/M/J/24
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(c) The diagram shows a regular pentagon with sides 15 cm.
(2w) cm 5(x + 7) cm
NOT TO
SCALE
15 cm (w + x + y) cm
15 cm
Work out the values of w, x and y.
w = ................................................
x = ................................................
y = ................................................ [5]
© UCLES 2024 0580/31/M/J/24 [Turn over
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