Equal chords of a circle subtend equal angles at the centre, prove it.

In the given circle, arc $APB$ and arc $BQC$ are in the ratio $2:5$ and $O$ is centre of the circle. If angle $AOB=44°$; find angle $AOC$.

In the given figure, $O$ is the centre of the given circle. $AB$ is a side of a square, $BC$ is a side of a regular pentagon and $CD$ is a side of a regular hexagon. Find $\angle AOB$.

In the given figure, $O$ is the centre of the given circle. $AB$ is a side of a square, $BC$ is a side of a regular pentagon and $CD$ is a side of a regular hexagon. Find $\angle AOC$.

In the given figure, $O$ is the centre of the given circle. $AB$ is a side of a square, $BC$ is a side of a regular pentagon and $CD$ is a side of a regular hexagon. Find $\angle AOD$.

In the given figure, $O$ is the centre of the given circle. $AB$ is a side of a square, $BC$ is a side of a regular pentagon and $CD$ is a side of a regular hexagon. Find $\angle BCD$.