Question

An arc of length 30 meters is formed by a central angle A on a circle of radius 15. The measure of A in degrees (to two decimal places) is.... 114.59 - right?

Answer 1

You were correct OP (at least on APEX)

Answer 2

An arc of length 30 m : l = 30 m.
r = 15 m,  ∠ A = ?
Formula for the length of an arc is:
 l = r π A / 180°  ( where A is the central angle )
A = l · 180 / r π = ( 30 · 180 ) / ( 15 · 3.1415926 ) = 114.43 °
This is very close to your result.