2025 MSHS PRELIMS P1 Q13

The diagram shows four points \(A\), \(B\), \(C\) and \(D\) which lie on the circumference of a circle with centre \(O\). \(BD\) is the diameter of the circle. Angle \(BDC=30^\circ\) and angle \(BCA=20^\circ\).

Find, giving reasons for each answer,

1. angle \(ABD\),[3]
2. angle \(ABC\).[2]