If the exterior angle of a regular polygon is equal to the acute angle of a right-angles isosceles triangle, then the polygon is a regular

pentagon

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hexagon

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octagon

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heptagon

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Solution

The correct option is C octagon
The acute angle of a right-angled isosceles $△ = 45^{o}$
$∴$ Each exterior angle of the regular polygon $= 45^{o}$
Hence, the number of sides of the regular polygon
${\frac{360^{o}}{45}}^{o} = 8$
Therefore, the given polygon is a $r e g u l a r o c t a g o n .$

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