Angle Subtended by an Arc of a Circle

In the given figure $O$ is the centre of the circle. Prove that $\angle x+\angle y=\angle z$

In the given figure $\text{'}O\text{'}$ is the center of the circle. $\angle AEB =130 °$ and $\angle EBC =20 °$, then find the value of $\angle BDA=$_____$°$.

The length of a chord of a circle is equal to its radius. If the measure of angle is $\text{'}k\text{'}$, subtended by this chord on the major segment, then find the value of $\text{'}k\text{'}?$

$\mathrm{O}$is the centre of the circle. $\mathrm{AOB}$ is a diameter. $\angle \mathrm{COB}=40°$, then the degree measure of semicircle $\mathrm{ACB}$_____$°$.

$\mathrm{O}$is the centre of the circle. $\mathrm{AOB}$ is a diameter. $\angle \mathrm{COB}=40°$, then the degree measure of minor arc $\mathrm{AC}$ _____$°$.

$\mathrm{O}$is the centre of the circle. $\mathrm{AOB}$ is a diameter. $\angle \mathrm{COB}=40°$, then the degree measure of major arc $\mathrm{AC}$ ____$°$.

$\mathrm{O}$is the centre of the circle. $\mathrm{AOB}$ is a diameter. $\angle \mathrm{COB}=40°$, then the degree measure of major arc $\mathrm{BC}$ is _____$°$ .

If $\angle \mathrm{PRQ} =45°$ in the figure, then find the value of $\angle \mathrm{PSQ}$:

$ABCDE$ is a pentagon inscribed in a circle, If$AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle EAD$.

$ABCDE$ is a pentagon inscribed in a circle, If $AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle AED$.

$ABCDE$ is a pentagon inscribed in a circle, If $AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle CDE$.

$ABCDE$ is a pentagon inscribed in a circle, If $AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle ABC$.

In given circle with centre $O$, the lengths of arc $PQ$ and arc $QR$ are in the ratio $3 : 2. \mathrm{If} \angle POQ = {96}^0,$ find $\angle PSQ$

In given circle with centre $O$, the lengths of arc $PQ$ and arc $QR$ are in the ratio $3 : 2. \mathrm{If} \angle POQ={96}^0,$ find $\angle RPQ$

In given figure, PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle PQR$.

In Fig. $13.47,$  PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle PRQ$

In given figure, PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle POQ$

In a regular pentagon $ABCDE$ inscribed in a circle, find the ratio between $\angle EDA$ and $\angle ADC$.

(Answer in the form $\frac{a}{b}$)

In given figure, chord $PQ=$ chord $RQ$. If $\angle POQ = 40°$, find the measure of $\angle QPR$.

$PQ$ is a diameter of the circle with centre $O$. If chord $PR=$chord $PS$, arc $PR=2$ arc $QR$, find $\angle PQR$.