Question

prove that the interior angle of a regular five sided polygon is three times the exterior angle of a regular decagon... ​

Answer 1

Step-by-step explanation:

Answer

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 = 3 x 36 = 108

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

= 108 = 108

Hence, proved !

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