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Let the angle be A.
complement of an angle A is   90 deg. -  A
supplement of that angle   is   180 deg  -  A

given the complement is  1/6 th of  supplement.
  =>   90 - A = 1/6 *(180 - A)
                  = 30 - A/ 6
         5A/6 = 60 deg.

   solving that A = 72 deg.
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modified... simple arithmetic equation,,,
Let the angle be X. Its compliment is 90 deg. - X. It's supplement is 180 deg - X. given the complement is 1/6 th of supplement. => 90 - X= 1/6 *(180 - X). On solving, we get X =72 degrees.
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