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Question

Which of the following is not true for an exterior angle of a regular polygon with n sides?


A

Each exterior angle =360°n

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B

Exterior angle =180° interior angle

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C

n=360°Exteriorangle

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D

Each exterior angle =n-2×180°n

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Solution

The correct option is D

Each exterior angle =n-2×180°n


Explanation for correct option:

Option(D):

Polygon: A closed plane figure bounded by straight lines.

Interior angle: An angle formed inside the two adjacent sides of a polygon as shown in the figure.

Exterior angle: When a side of a polygon is extended, then the angle formed outside the polygon is an exterior angle as shown in the figure.

The formula to find each interior angle of a regular polygon with n sides =n-2×180°n

Explanation for incorrect options

Options (A) and (C):

For a regular polygon with n sides

Exterior angle =360°n

n=360°Exteriorangle

Option(B):

If interior and exterior angle are forming linear pair, then

Interior angle + Exterior angle =180°

Exterior angle =180°-Interior angle.

Hence, the correct option is option(D)


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