Equation for arc measure given tangent segments and intercepted arcs.
Check the final answer first, then review the worked steps.
Step-by-step solution
The angle formed by two tangent segments from an external point to a circle is half the difference of the intercepted arcs. The angle at C is $53^\circ$. The intercepted arcs are $233^\circ$ and $x^\circ$. Thus, $\frac{1}{2}(233 - x) = 53$.
Answer
\frac{1}{2}(233 - x) = 53