Question

Each exterior angle of a polygon is 108 digree . How many sides does it have?

Answer 1

${\bold{{\blue{\underline{\red{G}\pink{iv}\green{en}\purple{:-}}}}}}$

• Interior angle = 108°
• Exterior angle = 180° - 108°
• Exterior angle = 72°

${\bold{{\blue{\underline{\red{Formula}\pink{\:to}\green{\:use{:-}}}}}}}$

• Sum of all exterior angles = 360°
• Number of exterior angles = $\frac{Sum\:of \:all \:exterior \:angles}{given\: exterior \:angle}$

${\bold{{\blue{\underline{\red{S}\pink{olu}\green{ti}\purple{on{:-}}}}}}}$

• Number of exterior angles = $\frac{Sum\: of \:all \:exterior\: angles}{given\: exterior \:angle}$
• Number of exterior angles = $\frac{360°}{72°}$
• Number of exterior angles = 5

${\therefore{\bold{{\blue{\underline{\red{The}\pink{\:Number\:of}\green{\:sides}\purple{\:are\:5}}}}}}}$