If one of the interior angles of a regular polygon is equal to 9/8 of each interior angle of a regular hexagon
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Total angle of a regular polygon
=(n-2)*180
Total angle of regular hexagon
=(6-2)*180
=4*180
=720
Then each interior angle of a regular hexagon =720/6=120
Then one interior angle of regular polygon =9/8*120=9*15=135
Exterior angle of this=180-135=45
Then number of sides of polygon =360/45=8sides
The regular polygon is octagon
=(n-2)*180
Total angle of regular hexagon
=(6-2)*180
=4*180
=720
Then each interior angle of a regular hexagon =720/6=120
Then one interior angle of regular polygon =9/8*120=9*15=135
Exterior angle of this=180-135=45
Then number of sides of polygon =360/45=8sides
The regular polygon is octagon
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Answer:
8 sides
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