Points A, B, C and D lie on a circle in that order. $\angle BAC = 35^\circ$ and $\angle CAD = 40^\circ$. What is $\angle BCD$?

Explanation

1. 01

   $\angle BAD = \angle BAC + \angle CAD = 35^\circ + 40^\circ = 75^\circ$.

2. 02

   ABCD is a cyclic quadrilateral, so $\angle BCD = 180^\circ - \angle BAD = 105^\circ$.

3. 03

   Check with angles in the same segment: $\angle BDC = \angle BAC = 35^\circ$ and $\angle DBC = \angle DAC = 40^\circ$, so $\angle BCD = 180^\circ - 75^\circ = 105^\circ$.