CAIE IGCSE Mathematics Extended Regular and Irregular Polygon Angles

Practise using interior and exterior angle sums to calculate unknown polygon angles, regular-polygon angles or the number of sides.

Exam points

calculate the interior-angle sum as (n − 2) × 180° and apply it to missing angles
use exterior angle 360° ÷ n or interior angle 180° − 360° ÷ n for a regular polygon
rearrange an angle formula to determine the number of sides and state the polygon name when asked

[Maximum number: 4]

A regular pentagon has an exterior angle, d.

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

$\frac35$ cao nfww
B3 for $\frac{72}{120}$ , or B2 for d=72 or h=120, or M1 for $360\div5$ oe or $180-(360\div6)$ oe

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E4.6.3 Know and use angle properties of regular and irregular polygons question 1