If 3 times the supplement of an angle is subtracted from 7 times the complement of the angle, the answer is the same as that obtained from trisecting a right angle. What is the supplement of this angle?

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Answer 1 · 2015-12-05T16:59:47

#165^@#

Let the unknown angle be #x#.

Hence the supplement of the angle is #180^@-x#.

The compliment of the angle is #90^@-x#.

Trisecting a right angle gives 3 angles of #30^@#.

Now writing an equation for the written information in the original question gives :

#7(90-x)-3(180-x)=30#

#therefore630-7x-540+3x=30#

#therefore x=(630-540-30)/(7-3)=15#

Therefore the supplement of the angle is #180-15=165^@#.