What is the measure of AC in the figure below?
Hint: We know that $\angle BAC=\frac12\cdot 118$. Then use that the sum of the angles in a triangle are $180$ and apply the inscribed angle theorem once more to finish. (I'll leave it to you to figure out where)
since BC is 118, that means that A is 59 degrees because of the inscribed angle theorem (i think thats the right theorem).
add A and C, which is 59 + 48, which is 107
since triangle angles add to 180, 180 - 107 is 73
because of the inscribed angle theorem again, AC is 146
Arc AB = 2 times the inscribed anlge = 2 * 48
then AC = 360 - 118 - 2* 48 = 146 o
+605 
