Question

If an angle is 30 more than its one half of its complimentary find its measure

Answer 1

x is the angle.
90 - x is its complement.
if the angle is 30 degree more than one half of its complement, then .....
x = 1/2 * (90 - x) + 30
simplify this to get x = 45 - 1/2 * x + 30
simplify further to get x = 75 - 1/2 * x
add 1/2 * x to both sides of this equation to get x + 1/2 * x = 75
simplify to get 1.5 * x = 75.
solve for x to get x = 75 / 1.5 = 50. 

the angle is 50 degrees.
its complement is 90 - 50 = 40 degrees.
the angle is 30 degrees more than half its complement.
half its complement is 20.
20 + 30 = 50

Answer 2

Let the angle be x
then it's complementary=90-x
then according to question
$x = 30 + \frac{1}{2} \times (90 - x) \\ 2x = 60 + 90 - x \\ 3x = 150 \\ x = 50$