Write 0.37373737... as a ratio of two relatively prime integers

What is the value of x in the diagram below?

Axel follows these steps to divide 40 by 9: start with 40. 1. divide by 9 and write down the remainder. 2. write a zero after the remainder. 3. repeat steps 1 and 2 until you have a remainder of zero. examine his work, and then complete the statements below.

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?