CAIE IGCSE Mathematics Extended Angle and Polygon Questions

Practise calculating and justifying angles using point, line, triangle, quadrilateral, parallel-line and regular-polygon properties.

Syllabus
2028–2030
Topic
E4.6
Level
Extended

Exam points

  • select the relevant point, line, triangle or quadrilateral angle sum before solving
  • use corresponding, alternate or co-interior facts only when the lines are established as parallel
  • calculate regular-polygon interior or exterior angles and use them to determine side counts

Covered syllabus points

E4.6.1 Calculate unknown angles and give simple explanations using theE4.6.2 Calculate unknown angles and give geometric explanations for anglesE4.6.3 Know and use angle properties of regular and irregular polygons

E4.6 Angles question 1

[Maximum number: 7]

Question (a)

(a)

The diagram shows three lines meeting at a point.

The ratio a: b: c=3: 4: 5.

Find the value of c.

Figure for Question (a) — CAIE IGCSE Mathematics Extended

NOT TO SCALE

c=
[ 3 ]

Question (b)

(b)

A regular pentagon has an exterior angle, d.

A regular hexagon has an interior angle, h.
Find the fraction dh\frac{d}{h}.
Give your answer in its simplest form.

[ 4 ]

E4.6 Angles question 2

[Maximum number: 3]
NOT TO SCALE

NOT TO SCALE

The diagram shows two straight lines intersecting two parallel lines.
Find the values of a, b and c.
a=b=c=\begin{aligned}a&=\\b&=\\c&=\end{aligned}

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