Question 7 — IGCSE 0580 May/June 2023 Paper 31
Cambridge IGCSE Mathematics 0580, Core tier, calculator. Topic: Geometry · Angles using geometrical properties. Worth 14 marks.
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Question text
7 (a)
D
F
NOT TO
SCALE
E
O
C
B
28°
A
The diagram shows a circle, centre O, with points B, D and E on the circumference.
AOEF is a straight line.
The straight line AC touches the circle at B.
(i) Write down the mathematical name for
(a) line BOD
................................................. [1]
(b) line ABC.
................................................. [1]
(ii) Write down the two geometrical reasons why angle AOBis62°.
.............................................................................................................................................
and ...................................................................................................................................... [2]
(iii) Give the geometrical reason why angle DOE is also 62°.
............................................................................................................................................. [1]
© UCLES 2023 0580/31/M/J/23
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(iv) (a) Find angle DEB.
Angle DEB = ................................................ [1]
(b) Find angle ODE.
Angle ODE = ................................................ [2]
(c) Find angle BEF.
Angle BEF = ................................................ [2]
(b) Write down two geometrical properties that show that a polygon is regular.
....................................................................... and ...................................................................... [2]
(c) Work out the interior angle of a regular 10-sided polygon.
................................................. [2]
© UCLES 2023 0580/31/M/J/23 [Turn over
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