Half the supplement of an angel is 12 degrees less than twice the complement of the angle. Find the measure of the angle.
I really nedd help on this one. I really don't know how to set it up.
2007-02-20 15:49:11 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let X be the angle you are looking for.
The Supplement is 180 - x
The Complement is 90 - x
Half the supplement is 12 degrees less than twice the complement
Half of 180 - x is 12 degrees less than twice 90 - x
(180 - x) / 2 is 12 degrees less than 2*(90 - x)
(180 - x) / 2 = 2*(90 - x) - 12
Multiply both sides by 2
180 - x = 4*(90 - x) - 24
Distribute
180 - x = 360 - 4x - 24
Moves the x's to one side
180 + 3x = 360 - 24
simplify all the numbers
3x = 156
x = 52
Angle is 52.
Check: Supplement is 128, Complement is 38
Half the supplement is 64. Double the Complement is 76. 64 is 12 less than 76. It works.
2007-02-20 15:56:40 · answer #1 · answered by Anonymous · 1⤊ 0⤋
1/2(180-x) = 2(90-x) -12 The brackets are the supplement and the complement
90-x/2=180 -2x -12 so 3/2*x=78 and x=52 degrees
2007-02-21 07:47:47 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋