What is the value of a + b? you may assume that the ray is tangent to the circle. 180 128 90 64

See the attached picture to better understand the problem

we know that
if the ray is tangent to the circle
then 
diameter ABC is perpendicular to ray FC
and  
the value of (a + b) is equal to 90 degrees

let's check it
step 1
find measure arc DC
arc DC=180-54-----> 126°
∠DBC=126°------> by central angle

step 2
find angle a°
we know that

The inscribed angle measures half of the arc it comprises.
so
∠a=arc AD/2----> 54/2--->∠a= 27°
∠b=arc DC/2----> 126/2---> ∠b=63°

∠a+∠b=27+63----> 90°------> is ok

the answer is
a+b is equal to 90 degrees