Question

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

Answer 1

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

Answer 2

we know that

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

so

`m\ angle\ BCA= (1)/(2) *(arc\ BOA-arc\ BA)\\\\ m\ angle\ BCA= (1)/(2) *(250-110)\\ \\ m\ angle\ BCA=70\ degrees`

therefore

the answer is

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