Explanation:
the sum of all angles around a single point on one side of a line is always 180°.
because that line can be seen as an extended diameter of a circle (which cuts the circle into 2 half-circles), with the given point being the center of the circle. then one side of the line is one of these half-circles, and a half-circle stand for 180°.
in our case the line is KM, the point is B.
we have on the upper side of KM 2 angles that together cover the complete side (without overlapping). so, together they must be 180° (supplementary angles).
and so we have
180 = (y + 10) + 125
55 = y + 10
y = 45
therefore,
angle KBC = y + 10 = 45 + 10 = 55°