Edexcel IGCSE Math A 4.2.D regular polygons

Practise regular-polygon questions by linking each exterior angle to 360 degrees and each interior angle to its supplement.

Exam points

Find the number of sides from an exterior angle by dividing 360 degrees.
Use interior and exterior angle relationships to form and solve equations.
Calculate n for a regular polygon when the angle information is given algebraically.

[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.

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4.2.D Regular polygons and their angles question 1