Answer :
'Complement' = difference between an angle an 90 degrees.
'Supplement' = difference between an angle and 180 degrees.
Complement of A = 90 - A
Supplement of A = 180 - A
The problem says that the complement is 1/6 of the supplement, right ?
So 90 - A = (1/6) x (180 - A)
Multiply each side of this equation by 6 :
540 - 6 A = 180 - A
Subtract 180 from each side:
360 - 6 A = - A
Add 6A to each side :
360 = 5 A
Divide each side by 5 :
A = 72°
'Supplement' = difference between an angle and 180 degrees.
Complement of A = 90 - A
Supplement of A = 180 - A
The problem says that the complement is 1/6 of the supplement, right ?
So 90 - A = (1/6) x (180 - A)
Multiply each side of this equation by 6 :
540 - 6 A = 180 - A
Subtract 180 from each side:
360 - 6 A = - A
Add 6A to each side :
360 = 5 A
Divide each side by 5 :
A = 72°