Find the angle..?

Question

4 times the measure of the complement of an angle is 12 more than twice the difference of the measures of its supplement and its complement. Find the angle.

Answer 1

Let the angle be 'x' , the complement 'y' and the supplement 'z'
It's obvious that z>y or
x + y = 90
x + z = 180
y = 90-x
z = 180 - x

4y = 2(z-y) + 12 (According to question)
4(90 - x) = 2[(180 - x) - (90 - x)] + 12
360 - 4x = 2(180 - x -90+x) + 12
360 -4x = 2(90) + 12
360 - 4x = 180 + 12
360 - 4x = 192
-4x = 192 - 360
-4x = -168
4x = 168
x = 168/4 = 42 degrees
The angle is 42 degrees

Answer 2

let the angle be x
complement of the angle = 90-x
supplement of the angle = 180-x
Difference of supplement and complement = (180-x) - (90-x)
= 180 - x -90 +x = 90
4(90-x) = 12 + 2*90 = 12 +180 =192
so, 90-x =192/4 = 48
so x = 90 - 48 = 42 the angle is 42 (degrees)
Check to see if answer is correct
the angle is 42
complement of the angle = 90-42 =48
supplement of the angle = 180-42 = 138
difference between supplement and complement = 138-48 = 90
is 4*48 = 12 + 2*90
is 192 = 12 +180 ?
..yes..the right hand side does add upto 192
so the angle being 42 (degrees ) is correct
[it is always good to check your answer wherever possible so that you can confirm that what you have got is the correct answer]

Answer 3

4(90-x)=2(90-x-180-x)+12

You can solve for x and find the angle because otherwise you wont learn .

Answer 4

suppose that angel is θ
4(90 - θ ) -12 = 2 ( (180 - θ ) - (90 - θ ) )
360 - 4θ - 12 = 180
4θ = 360 - 180 -12
4θ = 168
θ = 42°