x = 52
let x be the angle then (180 - x ) represents one half of the supplement of the angle and
2( 90 - x ) - 12 represents 12 less than twice the complement of the angle
equating these 2 expressions
(180 - x ) = 2(90 - x ) -12
distribute brackets on both sides
90 - x = 180 - 2x - 12 = 168 - 2x
add 2x to both sides
90 + x = 168 → ( subtract 90 from both sides )
x = 78
multiply both sides by 2 and divide by 3
x = 52