This problem can be solved with a simple proportion:
Angles Arcs
Part: central angle intercepted arc
----------------- = -------------------
Total: full circle (360) full circumference
(Since Algebra.com's software doesn't "do" theta, I am going to use q in place of theta. So replace any q's below with theta.)
Your proportion is, therefore:
(Since Circumference = 2*r*pi.)
This simplifies as follows:
To solve for q we start by cross-multiplying:
which simplifies to:
Next we divide by
The fraction reduces:
So q (or theta) is degrees.