Question 127317
The complement of an angle is 18 degrees more than 1/3 its supplement. find the measure of the angle.
:
The expression representing the complement of an angle (x):
(90 - x)
:
The expression representing the supplement of an angle (x)
(180 - x)
:
"the complement of an angle is 18 degrees more than 1/3 its supplement."
 (90 - x) = {{{1/3}}}(180-x) + 18
:
90 - x = 60 - {{{1/3}}}x + 18; found one third of 180
:
90 - x = 78 - {{{1/3}}}x
:
90 - 78 = -{{{1/3}}}x + x
:
12 = +{{{2/3}}}x
Multiply equation by 3 to get rid of the denominator
3(12) = 3*{{{2/3}}}x
36 = 2x
x = {{{36/2}}}
x = 18 degrees
:
:
Check solution using the statement:
"the complement of an angle is 18 degrees more than 1/3 its supplement."
(90 - 18) = {{{1/3}}}(180-18) + 18
72 = {{{1/3}}}*162 + 18
72 = 54 + 18