In the given figure, the centre $\mathrm{O}$ of the small circle lies on the circumference  of the bigger circle. If $\angle \mathrm{APB}=75°$ and $\angle \mathrm{BCD}=40°$, find :

$\angle \mathrm{ABD}$,

  

In the given figure, the centre $\mathrm{O}$ of the small circle lies on the circumference  of the bigger circle. If $\angle \mathrm{APB}=75°$ and $\angle \mathrm{BCD}=40°$, find :

$\angle \mathrm{ADB}$.

In the given figure, $\angle \mathrm{BAD}=65°, \angle \mathrm{ABD}=70°$ and $\angle \mathrm{BDC}=45°$. Find :

$\angle \mathrm{BCD}$

In the given figure, $\angle \mathrm{BAD}=65°, \angle \mathrm{ABD}=70°$ and $\angle \mathrm{BDC}=45°$. Find :

$\angle \mathrm{ACB}$

In a cyclic quadrilateral $\mathrm{ABCD}, \angle \mathrm{A}:\angle \mathrm{C}=3:1$ and $\angle \mathrm{B}:\angle \mathrm{D}=1:5$; find each angle of the quadrilateral.

The given figure shows a circle with centre $\mathrm{O}$ and $\angle \mathrm{ABP}=42°$.

Calculate the measure of ;

$\angle \mathrm{PQB}$

The given figure shows a circle with centre $\mathrm{O}$ and $\angle \mathrm{ABP}=42°$.

Calculate the measure of ;

$\angle \mathrm{QPB}+\angle \mathrm{PBQ}$

In the given figure, $\mathrm{M}$ is the centre of the circle. Chords $\mathrm{AB}$ and $\mathrm{CD}$ are perpendicular to each other. If $\angle \mathrm{MAD}=\mathrm{x}$ and $\angle \mathrm{BAC}\mathit{=}y$ ; Express $\angle \mathrm{AMD}$ in terms of $x.$

In the given figure, $\mathrm{M}$ is the centre of the circle. Chords $\mathrm{AB}$ and $\mathrm{CD}$ are perpendicular to each other. If $\angle \mathrm{MAD}=\mathrm{x}$ and $\angle \mathrm{BAC}\mathit{=}y$ ;

express $\angle \mathrm{ABD}$ in terms of $y.$