if an angle is 30° more than one half of its complement,find the measure of the angle

Let us assume that the angle is x.

Then,its complement will be 90-x.

30 degree more than one half of its complement, i.e 30+(90-x)/2

According to the sum,

x=30+(90-x)/2

x=60+90-x/2

x=150-x/2

2x=150-x

3x=150

x=50.

Hence the angle is 50.