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?

1 Answer
Dec 5, 2015

#165^@#

Explanation:

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^@#.