since BA ≅ BC, that means is an isosceles triangle, whose twin sides make twin angles at the base, namely the interior angles at A and C are both twin angles, and their exterior angles at those point are also twins, check the picture below.
that simply means that "x" and "y" are linear angles, therefore
x + y = 180°
117 + y = 180
y = 180 - 117
y = 63.