Find $\angle BOD$ in the given figure. Consider a circle with centre $O$. Two chords $AB$ and $CD$ extended intersect at a point $P$ outside the circle. If $\angle AOC=43^\circ$ and $\angle BPD=18^\circ$, then the value of $\angle BOD$ is ____?

Assuming that $AB=CD$ I have been able to deduce that it will be $7^\circ$. How to do the sum without the extra assumption?

Draw $AD$.  Then
$$ \angle BOD = 2\angle BAD = 2\angle PAD = 2(\angle ADC-\angle APD) = \angle AOC-2\angle APD = 7^\circ $$
