In the figure, $\mathrm{}\mathrm{\angle }\mathrm{A}\mathrm{B}\mathrm{C}={91}^0$ and $\mathrm{\angle }\mathrm{A}\mathrm{C}\mathrm{B}={29}^0.$ What is the measure of $\mathrm{\angle }\mathrm{B}\mathrm{D}\mathrm{C}$?

In the figure, if $\mathrm{O}\mathrm{}$ is the centre of the circle, then what is the measure of $\mathrm{\angle }\mathrm{A}\mathrm{D}\mathrm{C}?$

In the figure, $\mathrm{O}\mathrm{}$ is the centre of the circle and $\mathrm{P}\mathrm{R}=\mathrm{Q}\mathrm{R}.$ What is the measure of $\mathrm{\angle }\mathrm{P}\mathrm{Q}\mathrm{R}?$

In the given figure, $\mathrm{O}$ is the centre of the circle. If $\mathrm{\angle }\mathrm{O}\mathrm{A}\mathrm{B}=40°$, then what is the measure of $\mathrm{\angle }\mathrm{A}\mathrm{C}\mathrm{B}$?