Question

Point O is the center of the circle in the diagram. What is m∠BCA? 

Answer 1

we know that

The measure of the external angle is the semidifference of the arcs that it covers.

so

$m\ angle\ BCA= \frac{1}{2} *(arc\ BOA-arc\ BA)\\\\ m\ angle\ BCA= \frac{1}{2} *(250-110)\\ \\ m\ angle\ BCA=70\ degrees$

therefore

the answer is

The measure of angle BCA is equal to $70\ degrees$

Answer 2

As you know the exterior angle formed by m< BOA is 250 degrees.

The point where C is the point of vertical angles. Vertical angles form a linear pair.
Linear pair is Always of 180 degrees so,
250 - 180 = 70 degrees