Question

Prove that the interior angle of a regular five sided polygon (pentagon) is three times the exterior angle of a regular decagon.

Answer 1

A pentagon has five sides

One interior angle of a pentagon= (n-2)�180/n

One interior angle of a pentagon, where, n=5,

=>(5-2)�180/5

=>108�

All exterior angles of all polygons sum up to 360�

=> Each exterior angle of a decagon = 360/10, because decagon has 10 sides

=> Each exterior angle of a decagon = 36�

Therefore, 3 exterior angles of a decagon = 36�3 = 108�

3 exterior angles of a decagon = 1 interior angle of a pentagon

=> 108� = 108�

Hence, proved.

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Answer 2

Hence proved that the interior angle of a Pentagon is equal to three times of exterior angle of decagon=108°.

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