Edexcel IGCSE Math A 4.2 Polygons Question Bank

Practise naming polygons, using angle properties, and recognising regular, similar or congruent shapes from diagrams and grids.

Exam points

name polygons and quadrilaterals from side counts, diagrams or given shape properties
calculate missing interior or exterior angles using polygon and quadrilateral angle sums
recognise similar or congruent shapes, including matching letters or grid positions

Covered syllabus points

4.2.A Names of polygons 4.2.B Quadrilaterals and their angle sum 4.2.C Properties of quadrilaterals 4.2.D Regular polygons and their angles 4.2.E Angle sum of polygons 4.2.F Congruence as meaning the same shape and size 4.2.G Congruent polygons

[Maximum number: 4]

Diagram NOT accurately drawn

The diagram shows part of a regular n-sided polygon with
an interior angle of $(9 x+27)^{\circ}$
an exterior angle of $(2 x-23)^{\circ}$
Work out the value of n

Angles on a straight line:
(9x+27)+(2x-23)=180 $11x+4=180\quad\Rightarrow\quad x=16$
Exterior angle:
$2(16)-23=9^\circ$
Number of sides:
$n=\frac{360}{9}=40$

Final answer:
n=40

M marks for forming the angle equation, finding the exterior angle, and using 360/n. A1 cao.

[Maximum number: 3]

The diagram shows a pentagon.

Figure for Question 4.2 Polygons question 2 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

Work out the value of x

Sum of interior angles:
$3\times180^\circ=540^\circ$ 90+135+67+119+x=540411+x=540
Final answer:
$x=129^\circ$

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Covered syllabus points

4.2 Polygons question 1

4.2 Polygons question 2