Find the measure of each exterior angle of a regular

Question:

Find the measure of each exterior angle of a regular

(i) pentagon

(ii) hexagon

(iii) heptagon

(iv) decagon

(v) polygon of 15 sides.

Solution:

Exterior angle of an $n$-sided polygon $=\left(\frac{360}{n}\right)^{\circ}$

(i) For a pentagon: $n=5$

$\therefore\left(\frac{360}{n}\right)=\left(\frac{360}{5}\right)=72^{\circ}$

(ii) For a hexagon: $n=6$

$\therefore\left(\frac{360}{n}\right)=\left(\frac{300}{6}\right)=60^{\circ}$

(iii) For a heptagon: $n=7$

$\therefore\left(\frac{360}{n}\right)=\left(\frac{360}{7}\right)=51.43^{\circ}$

(iv) For a decagon: $n=10$

$\therefore\left(\frac{360}{n}\right)=\left(\frac{360}{10}\right)=36^{\circ}$

(v) For a polygon of 15 sides: $n=15$

$\therefore\left(\frac{360}{n}\right)=\left(\frac{360}{15}\right)=24^{\circ}$

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