Points A, B, C and D lie on a circle in that order, with $AB = BC$ and $\angle ABC = 110^\circ$. What is $\angle BDC$?

Explanation

1. 01

   $AB = BC$, so in triangle ABC, $\angle BAC = \angle BCA = (180^\circ - 110^\circ) \div 2 = 35^\circ$.

2. 02

   $\angle BDC$ and $\angle BAC$ stand on the same arc BC and lie in the same segment, so they are equal.

3. 03

   $\angle BDC = 35^\circ$.