One-half of the supplement of an angle is twelve less than twice the complement of the angle. find the angle.

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

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