Question 504114
A supplement of an angle is six more than three times the angle's complement. Write an equation to represent the problem and solve for the angle, its complement, and its supplement.
:
Let x = the angle
then
(180-x) = it's supplement
and
(90-x) = it's complement
:
The equation for the given statement:
(180-x) = 3(90-x) + 6
180 - x = 270 - 3x + 6
-x + 3x = 276 - 180
2x = 96
x = 96/2
x = 48 degrees is the angle
then
180 - 48 = 132 degrees is the supplement
and
90 - 48 = 42 degrees is the complement
;
:
Check our solutions in the given statement:
"A supplement of an angle is six more than three times the angle's complement."
132 = 3(42) + 6
132 = 126 + 6; confirms our solutions