Question

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

Answer 1

x = 52

let x be the angle then $\frac{1}{2}$ (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

$\frac{1}{2}$ (180 - x ) = 2(90 - x ) -12

distribute brackets on both sides

90 - $\frac{1}{2}$ x = 180 - 2x - 12 = 168 - 2x

add 2x to both sides

90 + $\frac{3}{2}$ x = 168 → ( subtract 90 from both sides )

$\frac{3}{2}$ x = 78

multiply both sides by 2 and divide by 3

x = 52